JEE Main & Advanced Mathematics Trigonometric Equations Question Bank

done Solution of trigonometrical equations Total Questions - 106

• question_answer1)
  If \[\sin \theta +\cos \theta =1\] then the general value of \[\theta \]is [MNR 1987; IIT 1981; Karnataka CET 2000, 03; DCE 2000]
  A)
  \[2n\pi \] done clear
  B)
  \[n\pi +{{(-1)}^{n}}\frac{\pi }{4}-\frac{\pi }{4}\] done clear
  C)
  \[2n\pi +\frac{\pi }{2}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer2)
  If \[{{\sin }^{2}}\theta =\frac{1}{4},\]then the most general value of \[\theta \]is  [MNR 1973; MP PET 1984, 90]
  A)
  \[2n\pi \pm {{(-1)}^{n}}\frac{\pi }{6}\] done clear
  B)
  \[\frac{n\pi }{2}\pm {{(-1)}^{n}}\frac{\pi }{6}\] done clear
  C)
  \[n\pi \pm \frac{\pi }{6}\] done clear
  D)
  \[2n\pi \pm \frac{\pi }{6}\] done clear
  View Solution play_arrow

• question_answer3)
  If \[{{\sec }^{2}}\theta =\frac{4}{3}\], then the general value of \[\theta \]is  [MP PET 1988]
  A)
  \[2n\pi \pm \frac{\pi }{6}\] done clear
  B)
  \[n\pi \pm \frac{\pi }{6}\] done clear
  C)
  \[2n\pi \pm \frac{\pi }{3}\] done clear
  D)
  \[n\pi \pm \frac{\pi }{3}\] done clear
  View Solution play_arrow

• question_answer4)
  General solution of the equation \[\cot \theta -\tan \theta =2\]is
  A)
  \[n\pi +\frac{\pi }{4}\] done clear
  B)
  \[\frac{n\pi }{2}+\frac{\pi }{8}\] done clear
  C)
  \[\frac{n\pi }{2}\pm \frac{\pi }{8}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer5)
  If \[\sqrt{3}\cos \,\theta +\sin \theta =\sqrt{2},\]then the most general value of \[\theta \] is                        [MP PET 1991, 2002;  UPSEAT 1999]
  A)
  \[n\pi +{{(-1)}^{n}}\frac{\pi }{4}\] done clear
  B)
  \[{{(-1)}^{n}}\frac{\pi }{4}-\frac{\pi }{3}\] done clear
  C)
  \[n\pi +\frac{\pi }{4}-\frac{\pi }{3}\] done clear
  D)
  \[n\pi +{{(-1)}^{n}}\frac{\pi }{4}-\frac{\pi }{3}\] done clear
  View Solution play_arrow

• question_answer6)
  If \[{{\sin }^{2}}\theta -2\cos \theta +\frac{1}{4}=0,\]then the general value of \[\theta \]is  [MP PET 1984]
  A)
  \[n\pi \pm \frac{\pi }{3}\] done clear
  B)
  \[2n\pi \pm \frac{\pi }{3}\] done clear
  C)
  \[2n\pi \pm \frac{\pi }{6}\] done clear
  D)
  \[n\pi \pm \frac{\pi }{6}\] done clear
  View Solution play_arrow

• question_answer7)
  If \[\sqrt{2}\sec \theta +\tan \theta =1,\] then the general value  \[\theta \]is  [MP PET 1989]
  A)
  \[n\pi +\frac{3\pi }{4}\] done clear
  B)
  \[2n\pi +\frac{\pi }{4}\] done clear
  C)
  \[2n\pi -\frac{\pi }{4}\] done clear
  D)
  \[2n\pi \pm \frac{\pi }{4}\] done clear
  View Solution play_arrow

• question_answer8)
  If \[2{{\tan }^{2}}\theta ={{\sec }^{2}}\theta ,\]then the general value of \[\theta \] is [MP PET 1989]
  A)
  \[n\pi +\frac{\pi }{4}\] done clear
  B)
  \[n\pi -\frac{\pi }{4}\] done clear
  C)
  \[n\pi \pm \frac{\pi }{4}\] done clear
  D)
  \[2n\pi \pm \frac{\pi }{4}\] done clear
  View Solution play_arrow

• question_answer9)
  If \[2\sin \theta +\tan \theta =0\], then the general values of \[\theta \] are
  A)
  \[2n\pi \pm \frac{\pi }{3}\] done clear
  B)
  \[n\pi ,2n\pi \pm \frac{2\pi }{3}\] done clear
  C)
  \[n\pi ,2n\pi \pm \frac{\pi }{3}\] done clear
  D)
  \[n\pi ,\,\,n\pi +\frac{2\pi }{3}\] done clear
  View Solution play_arrow

• question_answer10)
  If \[\sqrt{3}\tan 2\theta +\sqrt{3}\tan 3\theta +\tan 2\theta \tan 3\theta =1\], then the general value of\[\theta \]is
  A)
  \[n\pi +\frac{\pi }{5}\] done clear
  B)
  \[\left( n+\frac{1}{6} \right)\frac{\pi }{5}\] done clear
  C)
  \[\left( 2n\pm \frac{1}{6} \right)\frac{\pi }{5}\] done clear
  D)
  \[\left( n+\frac{1}{3} \right)\frac{\pi }{5}\] done clear
  View Solution play_arrow

• question_answer11)
  If \[\tan 2\theta \tan \theta =1\], then the general value of\[\theta \]is [Roorkee 1980; Karnataka CET 1992, 93, 2003]
  A)
  \[\left( n+\frac{1}{2} \right)\frac{\pi }{3}\] done clear
  B)
  \[\left( n+\frac{1}{2} \right)\,\pi \] done clear
  C)
  \[\left( 2n\pm \frac{1}{2} \right)\frac{\pi }{3}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer12)
  If \[1+\cot \theta =\text{cosec}\theta \], then the general value of \[\theta \] is  [Roorkee 1981]
  A)
  \[n\pi +\frac{\pi }{2}\] done clear
  B)
  \[2n\pi -\frac{\pi }{2}\] done clear
  C)
  \[2n\pi +\frac{\pi }{2}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer13)
  If \[\frac{1-\cos 2\theta }{1+\cos 2\theta }=3\], then the general value of\[\theta \]is
  A)
  \[2n\pi \pm \frac{\pi }{6}\] done clear
  B)
  \[n\pi \pm \frac{\pi }{6}\] done clear
  C)
  \[2n\pi \pm \frac{\pi }{3}\] done clear
  D)
  \[n\pi \pm \frac{\pi }{3}\] done clear
  View Solution play_arrow

• question_answer14)
  If \[3({{\sec }^{2}}\theta +{{\tan }^{2}}\theta )=5\], then the general value of \[\theta \] is
  A)
    \[2n\pi +\frac{\pi }{6}\] done clear
  B)
  \[2n\pi \pm \frac{\pi }{6}\] done clear
  C)
  \[n\pi \pm \frac{\pi }{6}\] done clear
  D)
  \[n\pi \pm \frac{\pi }{3}\] done clear
  View Solution play_arrow

• question_answer15)
  If \[\cos 7\theta =\cos \theta -\sin 4\theta \], then the general value of \[\theta \]is
  A)
  \[\frac{n\pi }{4},\frac{n\pi }{3}+\frac{\pi }{18}\] done clear
  B)
  \[\frac{n\pi }{3},\frac{n\pi }{3}+{{(-1)}^{n}}\frac{\pi }{18}\] done clear
  C)
  \[\frac{n\pi }{4},\frac{n\pi }{3}+{{(-1)}^{n}}\frac{\pi }{18}\] done clear
  D)
  \[\frac{n\pi }{6},\frac{n\pi }{3}+{{(-1)}^{n}}\frac{\pi }{18}\] done clear
  View Solution play_arrow

• question_answer16)
  If \[\frac{1-{{\tan }^{2}}\theta }{{{\sec }^{2}}\theta }=\frac{1}{2}\], then the general value of \[\theta \]is
  A)
  \[n\pi \pm \frac{\pi }{6}\] done clear
  B)
  \[n\pi +\frac{\pi }{6}\] done clear
  C)
  \[2n\pi \pm \frac{\pi }{6}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer17)
  If \[\cos \theta +\sec \theta =\frac{5}{2}\], then the general value of \[\theta \]is
  A)
  \[n\pi \pm \frac{\pi }{3}\] done clear
  B)
  \[2n\pi \pm \frac{\pi }{6}\] done clear
  C)
  \[n\pi \pm \frac{\pi }{6}\] done clear
  D)
  \[2n\pi \pm \frac{\pi }{3}\] done clear
  View Solution play_arrow

• question_answer18)
  If \[\cot \theta +\tan \theta =2\text{cosec}\theta \], the general value of \[\theta \] is  [Roorkee 1971]
  A)
  \[n\pi \pm \frac{\pi }{3}\] done clear
  B)
  \[n\pi \pm \frac{\pi }{6}\] done clear
  C)
  \[2n\pi \pm \frac{\pi }{3}\] done clear
  D)
    \[2n\pi \pm \frac{\pi }{6}\] done clear
  View Solution play_arrow

• question_answer19)
  If \[{{\tan }^{2}}\theta -(1+\sqrt{3})\tan \theta +\sqrt{3}=0\], then the general value of \[\theta \] is
  A)
  \[n\pi +\frac{\pi }{4},n\pi +\frac{\pi }{3}\] done clear
  B)
  \[n\pi -\frac{\pi }{4},n\pi +\frac{\pi }{3}\] done clear
  C)
  \[n\pi +\frac{\pi }{4},n\pi -\frac{\pi }{3}\] done clear
  D)
  \[n\pi -\frac{\pi }{4},n\pi -\frac{\pi }{3}\] done clear
  View Solution play_arrow

• question_answer20)
  The most general value of \[\theta \]satisfying the equations \[\sin \theta =\sin \alpha \]and \[\cos \theta =\cos \alpha \]is [IIT 1971; Karnataka CET 1993; DCE 1999]
  A)
  \[2n\pi +\alpha \] done clear
  B)
  \[2n\pi -\alpha \] done clear
  C)
  \[n\pi +\alpha \] done clear
  D)
  \[n\pi -\alpha \] done clear
  View Solution play_arrow

• question_answer21)
  a If \[4{{\sin }^{2}}\theta +2(\sqrt{3}+1)\cos \theta =4+\sqrt{3}\], then the general value  of \[\theta \]is
  A)
  \[2n\pi \pm \frac{\pi }{3}\] done clear
  B)
  \[2n\pi +\frac{\pi }{4}\] done clear
  C)
  \[n\pi \pm \frac{\pi }{3}\] done clear
  D)
  \[n\pi -\frac{\pi }{3}\] done clear
  View Solution play_arrow

• question_answer22)
  If \[\cot \theta +\cot \left( \frac{\pi }{4}+\theta  \right)=2\], then the general value  of  \[\theta \] is
  A)
  \[2n\pi \pm \frac{\pi }{6}\] done clear
  B)
  \[2n\pi \pm \frac{\pi }{3}\] done clear
  C)
  \[n\pi \pm \frac{\pi }{3}\] done clear
  D)
  \[n\pi \pm \frac{\pi }{6}\] done clear
  View Solution play_arrow

• question_answer23)
  If \[\cos 2\theta +3\cos \theta =0\], then the general value of \[\theta \] is
  A)
  \[2n\pi \pm {{\cos }^{-1}}\frac{-3+\sqrt{17}}{4}\] done clear
  B)
  \[2n\pi \pm {{\cos }^{-1}}\frac{-3-\sqrt{17}}{4}\] done clear
  C)
  \[n\pi \pm {{\cos }^{-1}}\frac{-3+\sqrt{17}}{4}\] done clear
  D)
  \[n\pi \pm {{\cos }^{-1}}\frac{-3-\sqrt{17}}{4}\] done clear
  View Solution play_arrow

• question_answer24)
  If \[\tan m\theta =\tan n\theta \], then the general value of \[\theta \] will be in [Pb. CET 2002]
  A)
  A. P. done clear
  B)
  G. P. done clear
  C)
  H. P. done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer25)
  If \[\tan \theta -\sqrt{2}\sec \theta =\sqrt{3}\], then the general value of   \[\theta \] is
  A)
  \[n\pi +{{(-1)}^{n}}\frac{\pi }{4}-\frac{\pi }{3}\] done clear
  B)
  \[n\pi +{{(-1)}^{n}}\frac{\pi }{3}-\frac{\pi }{4}\] done clear
  C)
  \[n\pi +{{(-1)}^{n}}\frac{\pi }{3}+\frac{\pi }{4}\] done clear
  D)
  \[n\pi +{{(-1)}^{n}}\frac{\pi }{4}+\frac{\pi }{3}\] done clear
  View Solution play_arrow

• question_answer26)
  If \[\sin \theta +\cos \theta =\sqrt{2}\cos \alpha \], then the general value of \[\theta \] is
  A)
  \[2n\pi -\frac{\pi }{4}\pm \,\,\alpha \] done clear
  B)
  \[2n\pi +\frac{\pi }{4}\pm \alpha \] done clear
  C)
  \[n\pi -\frac{\pi }{4}\pm \alpha \] done clear
  D)
  \[n\pi +\frac{\pi }{4}\pm \alpha \] done clear
  View Solution play_arrow

• question_answer27)
  If \[\tan \theta +\tan 2\theta +\tan 3\theta =\tan \theta \tan 2\theta \tan 3\theta \], then the general value of \[\theta \]is
  A)
  \[n\pi \] done clear
  B)
  \[\frac{n\pi }{6}\] done clear
  C)
  \[n\pi -\frac{\pi }{4}\pm \alpha \] done clear
  D)
  \[\frac{n\pi }{2}\] done clear
  View Solution play_arrow

• question_answer28)
  The solution of \[3\tan (A-{{15}^{o}})=\tan (A+{{15}^{o}})\] is
  A)
  \[n\pi +\frac{\pi }{4}\] done clear
  B)
  \[2n\pi +\frac{\pi }{4}\] done clear
  C)
  \[2n\pi -\frac{\pi }{4}\] done clear
  D)
  \[\frac{n\pi }{2}+{{(-1)}^{n}}\frac{\pi }{2}\] done clear
  View Solution play_arrow

• question_answer29)
  The general value of  satisfying the equation \[\tan \theta +\tan \left( \frac{\pi }{2}-\theta  \right)=2\], is [MNR 1974]
  A)
  \[n\pi +\frac{\pi }{4}\] done clear
  B)
  \[n\pi +\frac{\pi }{4}\] done clear
  C)
  \[2n\pi \pm \frac{\pi }{4}\] done clear
  D)
  \[n\pi +{{(-1)}^{n}}\frac{\pi }{4}\] done clear
  View Solution play_arrow

• question_answer30)
  If \[\cos 2\theta =(\sqrt{2}+1)\,\,\left( \cos \theta -\frac{1}{\sqrt{2}} \right)\], then the value of \[\theta \]is   [Roorkee 1977]
  A)
  \[2n\pi +\frac{\pi }{4}\] done clear
  B)
  \[2n\pi \pm \frac{\pi }{4}\] done clear
  C)
  \[2n\pi -\frac{\pi }{4}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer31)
  The general solution of the trigonometric equation \[\tan \theta =\cot \alpha \] is [MP PET 1994]
  A)
  \[\theta =n\pi +\frac{\pi }{2}-\alpha \] done clear
  B)
  \[\theta =n\pi -\frac{\pi }{2}+\alpha \] done clear
  C)
  \[\theta =n\pi +\frac{\pi }{2}+\alpha \] done clear
  D)
  \[\theta =n\pi -\frac{\pi }{2}-\alpha \] done clear
  View Solution play_arrow

• question_answer32)
  The solution of the equation \[\sec \theta -\text{cosec}\theta =\frac{4}{3}\] is   [Roorkee 1994]
  A)
  \[\frac{1}{2}[n\pi +{{(-1)}^{n}}{{\sin }^{-1}}(3/4)]\] done clear
  B)
  \[n\pi +{{(-1)}^{n}}{{\sin }^{-1}}(3/4)\] done clear
  C)
  \[\frac{n\pi }{2}+{{(-1)}^{n}}{{\sin }^{-1}}(3/4)\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer33)
  If \[\cos p\theta =\cos q\theta ,p\ne q\], then [MP PET 1995]
  A)
  \[\theta =2n\pi \] done clear
  B)
  \[\theta =\frac{2n\pi }{p\pm q}\] done clear
  C)
  \[\theta =\frac{n\pi }{p+q}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer34)
  The solution of the equation \[4{{\cos }^{2}}x+6\]\[{{\sin }^{2}}x=5\]  [AI CBSE 1983]
  A)
  \[x=n\pi \pm \frac{\pi }{2}\] done clear
  B)
  \[x=n\pi \pm \frac{\pi }{4}\] done clear
  C)
  \[x=n\pi \pm \frac{3\pi }{2}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer35)
  If \[\sin 3\alpha =4\sin \alpha \sin (x+\alpha )\sin (x-\alpha ),\]then \[x=\]
  A)
  \[n\pi \pm \frac{\pi }{6}\] done clear
  B)
  \[n\pi \pm \frac{\pi }{3}\] done clear
  C)
  \[n\pi \pm \frac{\pi }{4}\] done clear
  D)
  \[n\pi \pm \frac{\pi }{2}\] done clear
  View Solution play_arrow

• question_answer36)
  If \[\sin \text{ }\left( \frac{\pi }{4}\cot \theta  \right)=\cos \text{ }\left( \frac{\pi }{4}\tan \theta  \right)\,\,,\] then \[\theta =\]  [Pb. CET 1988]
  A)
  \[n\pi +\frac{\pi }{4}\] done clear
  B)
  \[2n\pi \pm \frac{\pi }{4}\] done clear
  C)
  \[n\pi -\frac{\pi }{4}\] done clear
  D)
  \[2n\pi \pm \frac{\pi }{6}\] done clear
  View Solution play_arrow

• question_answer37)
  The general value of \[\theta \]satisfying the equation \[2{{\sin }^{2}}\theta -3\sin \theta -2=0\] is  [Roorkee 1993]
  A)
  \[n\pi +{{(-1)}^{n}}\frac{\pi }{6}\] done clear
  B)
  \[n\pi +{{(-1)}^{n}}\frac{\pi }{2}\] done clear
  C)
  \[n\pi +{{(-1)}^{n}}\frac{5\pi }{6}\] done clear
  D)
  \[n\pi +{{(-1)}^{n}}\frac{7\pi }{6}\] done clear
  View Solution play_arrow

• question_answer38)
  The  general solution of the equation \[(\sqrt{3}-1)\sin \theta +(\sqrt{3}+1)\cos \theta =2\] is [Roorkee 1992]
  A)
  \[2n\pi \pm \frac{\pi }{4}+\frac{\pi }{12}\] done clear
  B)
  \[n\pi +{{(-1)}^{n}}\frac{\pi }{4}+\frac{\pi }{12}\] done clear
  C)
  \[2n\pi \pm \frac{\pi }{4}-\frac{\pi }{12}\] done clear
  D)
  \[n\pi +{{(-1)}^{n}}\frac{\pi }{4}-\frac{\pi }{12}\] done clear
  View Solution play_arrow

• question_answer39)
  The  general solution of \[\tan 3x=1\] is[Karnataka CET 1991]
  A)
  \[n\pi +\frac{\pi }{4}\] done clear
  B)
  \[\frac{n\pi }{3}+\frac{\pi }{12}\] done clear
  C)
  \[n\pi \] done clear
  D)
  \[n\pi \pm \frac{\pi }{4}\] done clear
  View Solution play_arrow

• question_answer40)
  The general solution of \[{{\sin }^{2}}\theta \sec \theta +\sqrt{3}\tan \theta =0\] is
  A)
  \[\theta =n\pi +{{(-1)}^{n+1}}\frac{\pi }{3},\theta =n\pi ,n\in Z\] done clear
  B)
  \[\theta =n\pi ,n\in Z\] done clear
  C)
  \[\theta =n\pi +{{(-1)}^{n+1}}\frac{\pi }{3},n\in Z\] done clear
  D)
  \[\theta =\frac{n\pi }{2},n\in Z\] done clear
  View Solution play_arrow

• question_answer41)
  General value of \[\theta \] satisfying the equation \[{{\tan }^{2}}\theta +\sec 2\theta -=1\] is [IIT 1996]
  A)
  \[m\pi ,n\pi +\frac{\pi }{3}\] done clear
  B)
  \[m\pi ,n\pi \pm \frac{\pi }{3}\] done clear
  C)
                  \[m\pi ,n\pi \pm \frac{\pi }{6}\] done clear
  D)
  None of these (Where m and n are integers) done clear
  View Solution play_arrow

• question_answer42)
  The general value \[\theta \] is obtained from the equation \[\cos 2\theta =\sin \alpha ,\] is [MP PET 1996]
  A)
  \[2\theta =\frac{\pi }{2}-\alpha \] done clear
  B)
  \[\theta =2n\pi \pm \left( \frac{\pi }{2}-\alpha  \right)\] done clear
  C)
  \[\theta =\frac{n\pi +{{(-1)}^{n}}\alpha }{2}\] done clear
  D)
  \[\theta =n\pi \pm \left( \frac{\pi }{4}-\frac{\alpha }{2} \right)\] done clear
  View Solution play_arrow

• question_answer43)
  \[\sin 6\theta +\sin 4\theta +\sin 2\theta =0,\]then \[\theta =\] [MP PET 1999; Pb. CET 2000]
  A)
  \[\frac{n\pi }{4}\]or \[n\pi \pm \frac{\pi }{3}\] done clear
  B)
  \[\frac{n\pi }{4}\]or \[n\pi \pm \frac{\pi }{6}\] done clear
  C)
  \[\frac{n\pi }{4}\]or \[2n\pi \pm \frac{\pi }{6}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer44)
  The general value of \[\theta \] satisfying \[{{\sin }^{2}}\theta +\sin \theta =2\] is [AMU 1996, 99]
  A)
  \[n\pi +{{(-1)}^{n}}\frac{\pi }{6}\] done clear
  B)
  \[2n\pi +\frac{\pi }{4}\] done clear
  C)
  \[n\pi +{{(-1)}^{n}}\frac{\pi }{2}\] done clear
  D)
  \[n\pi +{{(-1)}^{n}}\frac{\pi }{3}\] done clear
  View Solution play_arrow

• question_answer45)
  General solution of \[\tan 5\theta =\cot 2\theta \] is  [Karnataka CET 2000; Pb. CET 2001]
  A)
  \[\theta =\frac{n\pi }{7}+\frac{\pi }{14}\] done clear
  B)
   \[\theta =\frac{n\pi }{7}+\frac{\pi }{5}\] done clear
  C)
  \[\theta =\frac{n\pi }{7}+\frac{\pi }{2}\] done clear
  D)
  \[\theta =\frac{n\pi }{7}+\frac{\pi }{3},n\in Z\] done clear
  View Solution play_arrow

• question_answer46)
  The equation \[3{{\sin }^{2}}x+10\cos x-6=0\] is satisfied, if  [UPSEAT 2001]
  A)
  \[x=n\pi \pm {{\cos }^{-1}}(1/3)\] done clear
  B)
  \[x=2n\pi \pm {{\cos }^{-1}}(1/3)\] done clear
  C)
  \[x=n\pi \pm {{\cos }^{-1}}(1/6)\] done clear
  D)
  \[x=2n\pi \pm {{\cos }^{-1}}(1/6)\] done clear
  View Solution play_arrow

• question_answer47)
  If \[\cos \theta +\cos 2\theta +\cos 3\theta =0\], then the general value of \[\theta \] is [UPSEAT 2003]
  A)
  \[\theta =2m\pi \pm \frac{2\pi }{3}\] done clear
  B)
  \[\theta =2m\pi \pm \frac{\pi }{4}\] done clear
  C)
  \[\theta =m\pi \pm {{(-1)}^{m}}\frac{2\pi }{3}\] done clear
  D)
  \[x=m\pi +{{(-1)}^{m}}\frac{\pi }{3}\] done clear
  View Solution play_arrow

• question_answer48)
  The general value of \[\theta \] in the equation \[2\sqrt{3}\cos \theta =\tan \theta \],  is [MP PET 2003]
  A)
  \[2n\pi \pm \frac{\pi }{6}\] done clear
  B)
  \[2n\pi \pm \frac{\pi }{4}\] done clear
  C)
  \[n\pi +{{(-1)}^{n}}\frac{\pi }{3}\] done clear
  D)
  \[n\pi +{{(-1)}^{n}}\frac{\pi }{4}\] done clear
  View Solution play_arrow

• question_answer49)
  If \[\left| \,\begin{matrix}    \cos (A+B) & -\sin (A+B) & \cos 2B  \\    \sin A & \cos A & \sin B  \\    -\cos A & \sin A & \cos B  \\ \end{matrix}\, \right|=0\], then B = [EAMCET 2003]
  A)
  \[(2n+1)\frac{\pi }{2}\] done clear
  B)
  \[n\pi \] done clear
  C)
  \[(2n+1)\frac{\pi }{2}\] done clear
  D)
  \[2n\pi \] done clear
  View Solution play_arrow

• question_answer50)
  If \[\sin 2\theta =\cos 3\theta \]and \[\theta \]is an acute angle, then \[\sin \theta \]is equal to [EAMCET 1980]
  A)
  \[\frac{\sqrt{5}-1}{4}\] done clear
  B)
  \[\frac{-\sqrt{5}-1}{4}\] done clear
  C)
  0 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer51)
  If \[4{{\sin }^{4}}x+{{\cos }^{4}}x=1,\]then x = [Roorkee 1989]
  A)
  \[n\pi \] done clear
  B)
  \[n\pi \pm {{\sin }^{-1}}\frac{2}{5}\] done clear
  C)
  \[n\pi +\frac{\pi }{6}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer52)
  If \[\cos 3x+\sin \left( 2x-\frac{7\pi }{6} \right)=-2\], then \[x=\] (where \[k\in Z\])
  A)
  \[\frac{\pi }{3}(6k+1)\] done clear
  B)
  \[\frac{\pi }{3}(6k+1)\] done clear
  C)
  \[\frac{\pi }{3}(2k+1)\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer53)
  The solution of the equation \[\left| \,\begin{matrix}    \cos \theta  & \sin \theta  & \cos \theta   \\    -\sin \theta  & \cos \theta  & \sin \theta   \\    -\cos \theta  & -\sin \theta  & \cos \theta   \\ \end{matrix}\, \right|=0\], is [AMU 2002]
  A)
  \[\theta =n\pi \] done clear
  B)
  \[\theta =2n\pi \pm \frac{\pi }{2}\] done clear
  C)
  \[\theta =n\pi \pm {{(-1)}^{n}}\frac{\pi }{4}\] done clear
  D)
  \[\theta =2n\pi \pm \frac{\pi }{4}\] done clear
  View Solution play_arrow

• question_answer54)
  The set of values of x for which the expression \[\frac{\tan 3x-\tan 2x}{1+\tan 3x\tan 2x}=1\], is  [MP PET 1992; MNR 1993; UPSEAT 2002]
  A)
  \[\varphi \] done clear
  B)
  \[\frac{\pi }{4}\] done clear
  C)
  \[\left\{ n\pi +\frac{\pi }{4}:n=1,\,2,\,3..... \right\}\] done clear
  D)
  \[\left\{ 2n\pi +\frac{\pi }{4}:n=1,\,2,\,3..... \right\}\] done clear
  View Solution play_arrow

• question_answer55)
  If \[\tan \theta +\tan 2\theta +\sqrt{3}\tan \theta \tan 2\theta =\sqrt{3},\]then [UPSEAT 2001]
  A)
  \[\theta =(6n+1)\pi /18,\,\forall n\in I\] done clear
  B)
  \[\theta =(6n+1)\pi /9,\,\forall n\in I\] done clear
  C)
  \[\theta =(3n+1)\pi /9,\,\forall n\in I\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer56)
  The roots of the equation \[1-\cos \theta =\sin \theta .\sin \frac{\theta }{2}\]is [Orissa JEE 2004]
  A)
  \[k\pi ,k\in I\] done clear
  B)
  \[2k\pi ,k\in I\] done clear
  C)
  \[k\frac{\pi }{2},k\in I\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer57)
  If \[\frac{\tan 3\theta -1}{\tan 3\theta +1}=\sqrt{3}\], then the general value of \[\theta \]is  [MP PET 2004; Orissa JEE 2004]
  A)
  \[\frac{n\pi }{3}+\frac{\pi }{12}\] done clear
  B)
  \[\frac{n\pi }{3}+\frac{7\pi }{36}\] done clear
  C)
  \[n\pi +\frac{7\pi }{12}\] done clear
  D)
  \[n\pi +\frac{\pi }{12}\] done clear
  View Solution play_arrow

• question_answer58)
  If \[2{{\cos }^{2}}x+3\sin x-3=0,\,\,0\le x\le {{180}^{o}}\], then x = [MP PET 1986]
  A)
  \[{{30}^{o}},{{90}^{o}},{{150}^{o}}\] done clear
  B)
  \[{{60}^{o}},{{120}^{o}},{{180}^{o}}\] done clear
  C)
  \[{{0}^{o}},{{30}^{o}},{{150}^{o}}\] done clear
  D)
  \[{{45}^{o}},{{90}^{o}},{{135}^{o}}\] done clear
  View Solution play_arrow

• question_answer59)
  The equation \[\sin x+\cos x=2\]has [EAMCET 1986; MP PET 1998; Pb. CET 1993]
  A)
  One solution done clear
  B)
  Two solutions done clear
  C)
  Infinite number of solutions done clear
  D)
  No solutions done clear
  View Solution play_arrow

• question_answer60)
  The number of values of \[\theta \] in [0, 2p] satisfying the equation \[2{{\sin }^{2}}\theta =4+3\]\[\cos \theta \]are [MP PET 1989]
  A)
  0 done clear
  B)
  1 done clear
  C)
  2 done clear
  D)
  3 done clear
  View Solution play_arrow

• question_answer61)
  The equation \[\sin x\cos x=2\]has
  A)
  One solution done clear
  B)
  Two solutions done clear
  C)
  Infinite solutions done clear
  D)
  No solutions done clear
  View Solution play_arrow

• question_answer62)
  The number of solutions of the given equation \[\tan \theta +\sec \theta =\sqrt{3},\] where \[0<\theta <2\pi \]is
  A)
  0 done clear
  B)
  1 done clear
  C)
  2 done clear
  D)
  3 done clear
  View Solution play_arrow

• question_answer63)
  If \[\sin 5x+\sin 3x+\sin x=0\], then the value of x other than 0 lying between \[0\le x\le \frac{\pi }{2}\]is [MNR 1985]
  A)
  \[\frac{\pi }{6}\] done clear
  B)
  \[\frac{\pi }{12}\] done clear
  C)
  \[\frac{\pi }{3}\] done clear
  D)
  \[\frac{\pi }{4}\] done clear
  View Solution play_arrow

• question_answer64)
  One root of the equation \[\cos x-x+\frac{1}{2}=0\]lies in the interval [Kurukshetra CEE 1996]
  A)
  \[\left[ 0,\,\frac{\pi }{2} \right]\] done clear
  B)
  \[\left[ -\frac{\pi }{2},\,0 \right]\] done clear
  C)
  \[\left[ \frac{\pi }{2},\,\pi  \right]\] done clear
  D)
  \[\left[ \pi ,\frac{3\pi }{2} \right]\] done clear
  View Solution play_arrow

• question_answer65)
  If \[\sec x\cos 5x+1=0\], where \[0<x<2\pi \], then x = [Roorkee 1978; IIT 1963]
  A)
  \[\frac{\pi }{5},\frac{\pi }{5}\] done clear
  B)
  \[\frac{\pi }{5}\] done clear
  C)
  \[\frac{\pi }{4}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer66)
  The equation \[{{\sin }^{4}}x+{{\cos }^{4}}x+\sin 2x+\alpha =0\]is solvable for
  A)
  \[-\frac{1}{2}\le \alpha \le \frac{1}{2}\] done clear
  B)
  \[-3\le \alpha \le 1\] done clear
  C)
  \[-\frac{3}{2}\le \alpha \le \frac{1}{2}\] done clear
  D)
  \[-1\le \alpha \le 1\] done clear
  View Solution play_arrow

• question_answer67)
  If \[|k|\,=5\]and \[{{0}^{o}}\le \theta \le {{360}^{o}}\], then the number of different solutions of 3\[\cos \theta +4\sin \theta =k\] is
  A)
  Zero done clear
  B)
  Two done clear
  C)
  One done clear
  D)
  Infinite done clear
  View Solution play_arrow

• question_answer68)
  The number of values of x in the interval [0, 5\[\pi \]] satisfying the equation  \[3{{\sin }^{2}}x-7\sin x+2=0\]is [IIT 1998; MP PET 2000; Pb. CET 2003]
  A)
  0 done clear
  B)
  5 done clear
  C)
  6 done clear
  D)
  10 done clear
  View Solution play_arrow

• question_answer69)
  The equation \[\sqrt{3}\sin x+\cos x=4\]has  [EAMCET 2001]
  A)
  Only one solution done clear
  B)
  Two solutions done clear
  C)
  Infinitely many solutions done clear
  D)
  No solution done clear
  View Solution play_arrow

• question_answer70)
  The equation \[3\cos x+4\sin x=6\]has [Orissa JEE 2002]
  A)
  Finite solution done clear
  B)
  Infinite solution done clear
  C)
  One solution done clear
  D)
  No solution done clear
  View Solution play_arrow

• question_answer71)
  The equation \[\sin x+\sin y+\sin z=-3\] for \[0\le x\le 2\pi ,\] \[0\le y\le 2\pi ,\] \[0\le z\le 2\pi \], has [Orissa JEE 2003]
  A)
  One solution done clear
  B)
  Two sets of solutions done clear
  C)
  Four sets of solutions done clear
  D)
  No solution done clear
  View Solution play_arrow

• question_answer72)
  If \[\sin 2\theta =\cos \theta ,\,\,0<\theta <\pi \], then the possible values of \[\theta \] are
  A)
  \[{{90}^{o}},{{60}^{o}},{{30}^{o}}\] done clear
  B)
  \[{{90}^{o}},{{150}^{o}},{{60}^{o}}\] done clear
  C)
  \[{{90}^{o}},{{45}^{o}},{{150}^{o}}\] done clear
  D)
  \[{{90}^{o}},{{30}^{o}},{{150}^{o}}\] done clear
  View Solution play_arrow

• question_answer73)
  If \[2{{\sin }^{2}}\theta =3\cos \theta ,\]where \[0\le \theta \le 2\pi \], then \[\theta =\] [IIT 1963]
  A)
  \[\frac{\pi }{6},\frac{7\pi }{6}\] done clear
  B)
  \[\frac{\pi }{3},\frac{5\pi }{3}\] done clear
  C)
  \[\frac{\pi }{3},\frac{7\pi }{3}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer74)
  If                                                                                     , where \[0<\theta <{{180}^{o}}\], then \[\theta \] =
  A)
  \[{{30}^{o}},{{45}^{o}}\] done clear
  B)
  \[{{45}^{o}},{{90}^{o}}\] done clear
  C)
  \[{{135}^{o}},{{150}^{o}}\] done clear
  D)
   \[{{30}^{o}},{{45}^{o}},{{90}^{o}},{{135}^{o}},{{150}^{o}}\] done clear
  View Solution play_arrow

• question_answer75)
  Values of \[\theta (0<\theta <{{360}^{o}})\] satisfying \[\text{cosec}\theta +2=0\] are  [EAMCET 1994]
  A)
  \[{{210}^{o}},{{300}^{o}}\] done clear
  B)
  \[{{240}^{o}},{{300}^{o}}\] done clear
  C)
  \[{{210}^{o}},{{240}^{o}}\] done clear
  D)
  \[{{210}^{o}},{{330}^{o}}\] done clear
  View Solution play_arrow

• question_answer76)
  \[2{{\sin }^{2}}x+{{\sin }^{2}}2x=2,\,-\pi <x<\pi ,\]then \[x=\] [ISM Dhanbad 1989]
  A)
  \[\pm \frac{\pi }{6}\] done clear
  B)
  \[\pm \frac{\pi }{4}\] done clear
  C)
  \[\frac{3\pi }{2}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer77)
  The values of \[\theta \] satisfying \[\sin 7\theta =\sin 4\theta -\sin \theta \] and \[0<\theta <\frac{\pi }{2}\] are [EAMCET 1990]
  A)
  \[\frac{\pi }{9},\frac{\pi }{4}\] done clear
  B)
  \[\frac{\pi }{3},\frac{\pi }{9}\] done clear
  C)
  \[\frac{\pi }{6},\frac{\pi }{9}\] done clear
  D)
  \[\frac{\pi }{3},\frac{\pi }{4}\] done clear
  View Solution play_arrow

• question_answer78)
  The expression \[(1+\tan x+{{\tan }^{2}}x)\] \[(1-\cot x+{{\cot }^{2}}x)\] has the positive values for x, given by
  A)
  \[0\le x\le \frac{\pi }{2}\] done clear
  B)
  \[0\le x\le \pi \] done clear
  C)
  For all \[x\in R\] done clear
  D)
  \[x\ge 0\] done clear
  View Solution play_arrow

• question_answer79)
  If \[5\cos 2\theta +2{{\cos }^{2}}\frac{\theta }{2}+1=0,-\pi <\theta <\pi \], then \[\theta =\]  [Roorkee 1984]
  A)
  \[\frac{\pi }{3}\] done clear
  B)
  \[\frac{\pi }{3},{{\cos }^{-1}}\frac{3}{5}\] done clear
  C)
  \[{{\cos }^{-1}}\frac{3}{5}\] done clear
  D)
  \[\frac{\pi }{3},\pi -{{\cos }^{-1}}\frac{3}{5}\] done clear
  View Solution play_arrow

• question_answer80)
  If \[\cos \theta =\frac{-1}{2}\]and \[{{0}^{o}}<\theta <{{360}^{o}}\], then the values of \[\theta \]are   [Karnataka CET 2001]
  A)
  \[{{120}^{o}}\]and \[{{300}^{o}}\] done clear
  B)
  \[{{60}^{o}}\]and \[{{120}^{o}}\] done clear
  C)
  \[{{120}^{o}}\]and \[{{240}^{o}}\] done clear
  D)
  \[{{60}^{o}}\]and \[{{240}^{o}}\] done clear
  View Solution play_arrow

• question_answer81)
  If \[(2\cos x-1)(3+2\cos x)=0,\,0\le x\le 2\pi \], then \[x=\]    [MNR 1988; UPSEAT 2000]
  A)
  \[\frac{\pi }{3}\] done clear
  B)
  \[\frac{\pi }{3},\frac{5\pi }{3}\] done clear
  C)
  \[\frac{\pi }{2},\frac{5\pi }{3},{{\cos }^{-1}}\left( -\frac{3}{2} \right)\] done clear
  D)
  \[\frac{5\pi }{3}\] done clear
  View Solution play_arrow

• question_answer82)
  If \[0\le x\le \pi \]and \[{{81}^{{{\sin }^{2}}x}}+{{81}^{{{\cos }^{2}}x}}=30\], then x = [Karnataka CET 2004]
  A)
  \[\pi /6\] done clear
  B)
  \[\pi /2\] done clear
  C)
  \[\pi /4\] done clear
  D)
  \[3\pi /4\] done clear
  View Solution play_arrow

• question_answer83)
  If \[\sin \theta =\sqrt{3}\cos \theta ,-\pi <\theta <0\], then \[\theta =\] [MP PET 1992]
  A)
  \[-\frac{5\pi }{6}\] done clear
  B)
  \[-\frac{4\pi }{6}\]\[\] done clear
  C)
  \[\frac{4\pi }{6}\] done clear
  D)
  \[\frac{5\pi }{6}\] done clear
  View Solution play_arrow

• question_answer84)
  The value of \[\theta \] in between \[{{0}^{o}}\]and \[{{360}^{o}}\]and satisfying the equation \[\tan \theta +\frac{1}{\sqrt{3}}=0\]is equal to  [Pb. CET 2002]
  A)
  \[\theta ={{150}^{o}}\]and \[{{300}^{o}}\] done clear
  B)
  \[\theta ={{120}^{o}}\]and \[{{300}^{o}}\] done clear
  C)
  \[\theta ={{60}^{o}}\]and \[{{240}^{o}}\] done clear
  D)
  \[\theta ={{150}^{o}}\]and \[{{330}^{o}}\] done clear
  View Solution play_arrow

• question_answer85)
  The solution of equation \[{{\cos }^{2}}\theta +\sin \theta +1=0\] lies in the interval       [UPSEAT 2004; IIT 1992]
  A)
  \[\left( -\frac{\pi }{4},\frac{\pi }{4} \right)\] done clear
  B)
  \[\left( \frac{\pi }{4},\frac{3\pi }{4} \right)\] done clear
  C)
  \[\left( \frac{3\pi }{4},\frac{5\pi }{4} \right)\] done clear
  D)
  \[\left( \frac{5\pi }{4},\frac{7\pi }{4} \right)\] done clear
  View Solution play_arrow

• question_answer86)
  The number of solution of the equation \[2\cos ({{e}^{x}})={{5}^{x}}+{{5}^{-x}}\], are          [UPSEAT 2004; IIT 1992]
  A)
  No solution done clear
  B)
  One solution done clear
  C)
  Two solutions done clear
  D)
  Infinitely many solutions done clear
  View Solution play_arrow

• question_answer87)
  The most general value of \[\theta \]satisfying the equations \[\tan \theta =-1\] and  \[\cos \theta =\frac{1}{\sqrt{2}}\]is [MNR 1982; Roorkee 1990; UPSEAT 2002; MP PET 2003]
  A)
  \[n\pi +\frac{7\pi }{4}\] done clear
  B)
  \[n\pi +{{(-1)}^{n}}\frac{7\pi }{4}\] done clear
  C)
  \[2n\pi +\frac{7\pi }{4}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer88)
  The most general value of \[\theta \]which will satisfy both the equations \[\sin \theta =-\frac{1}{2}\]and \[\tan \theta =\frac{1}{\sqrt{3}}\]is [MNR 1980; MP PET 1989; DCE 1995]
  A)
  \[n\pi +{{(-1)}^{n}}\frac{\pi }{6}\] done clear
  B)
  \[n\pi +\frac{\pi }{6}\] done clear
  C)
  \[2n\pi \pm \frac{\pi }{6}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer89)
  Common roots of the equations \[2{{\sin }^{2}}x+{{\sin }^{2}}2x=2\] and  \[\sin 2x+\cos 2x=\tan x,\] are
  A)
  \[x=(2n-1)\frac{\pi }{2}\] done clear
  B)
  \[x=(2n+1)\frac{\pi }{4}\] done clear
  C)
  \[x=(2n+1)\frac{\pi }{3}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer90)
  If \[r\,\sin \theta =3,r=4(1+\sin \theta ),\,\,0\le \theta \le 2\pi ,\]then \[\theta =\] [Roorkee 1974]
  A)
  \[\frac{\pi }{6},\frac{\pi }{3}\] done clear
  B)
  \[\frac{\pi }{6},\frac{5\pi }{6}\] done clear
  C)
  \[\frac{\pi }{3},\frac{\pi }{4}\] done clear
  D)
  \[\frac{\pi }{2},\pi \] done clear
  View Solution play_arrow

• question_answer91)
  If \[\cos \theta =-\frac{1}{\sqrt{2}}\]and \[\tan \theta =1\], then the general value of \[\theta \]is
  A)
  \[2n\pi +\frac{\pi }{4}\] done clear
  B)
  \[(2n+1)\,\pi +\frac{\pi }{4}\] done clear
  C)
  \[n\pi +\frac{\pi }{4}\] done clear
  D)
  \[n\pi \pm \frac{\pi }{4}\] done clear
  View Solution play_arrow

• question_answer92)
  If \[\sin (A+B)\]=1 and \[\cos (A-B)=\frac{\sqrt{3}}{2},\]then the smallest positive values of A and B are
  A)
  \[{{60}^{o}},\text{ }{{30}^{o}}\] done clear
  B)
  \[{{75}^{o}},\text{ }{{15}^{o}}\] done clear
  C)
  \[{{45}^{o}},\text{ }{{60}^{o}}\] done clear
  D)
  \[{{45}^{o}},\text{ }{{45}^{o}}\] done clear
  View Solution play_arrow

• question_answer93)
  The smallest positive angle which satisfies the equation \[2{{\sin }^{2}}\theta +\sqrt{3}\cos \theta +1=0\], is [ISM Dhanbad 1972; MP PET 1993]
  A)
  \[\frac{5\pi }{6}\] done clear
  B)
  \[\frac{2\pi }{3}\] done clear
  C)
  \[\frac{\pi }{3}\] done clear
  D)
  \[\frac{\pi }{6}\] done clear
  View Solution play_arrow

• question_answer94)
  \[\cot \theta =\sin 2\theta (\theta \ne n\pi \], n is integer), if \[\theta =\] [BIT Ranchi 1991; Pb. CET 1991]
  A)
  \[{{45}^{o}}\] and \[{{60}^{o}}\] done clear
  B)
  \[{{45}^{o}}\]and \[{{90}^{o}}\] done clear
  C)
  \[{{45}^{o}}\]only done clear
  D)
  \[{{90}^{o}}\]only done clear
  View Solution play_arrow

• question_answer95)
  The value of \[\theta \] satisfying the given equation \[\cos \theta +\sqrt{3}\sin \theta \] = 2, is   [MNR 1981; EAMCET 1989]
  A)
  \[\frac{\pi }{3}\] done clear
  B)
  \[\frac{5\pi }{3}\] done clear
  C)
  \[\frac{2\pi }{3}\] done clear
  D)
  \[\frac{4\pi }{3}\] done clear
  View Solution play_arrow

• question_answer96)
  If \[\cos A\sin \left( A-\frac{\pi }{6} \right)\]is maximum, then the value of A is equal to
  A)
  \[\frac{\pi }{3}\] done clear
  B)
  \[\frac{\pi }{4}\] done clear
  C)
  \[\frac{\pi }{2}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer97)
  If \[\cos {{40}^{o}}=x\] and \[\cos \theta =1-2{{x}^{2}}\], then the possible values  of \[\theta \]lying between \[{{0}^{o}}\]and \[{{360}^{o}}\]is
  A)
  \[{{100}^{o}}\]and \[{{260}^{o}}\] done clear
  B)
  \[{{80}^{o}}\]and\[{{280}^{o}}\] done clear
  C)
  \[{{280}^{o}}\]and \[{{110}^{o}}\] done clear
  D)
  \[{{110}^{o}}\]and \[{{260}^{o}}\] done clear
  View Solution play_arrow

• question_answer98)
  The only value of x for which \[{{2}^{\sin x}}+{{2}^{\cos x}}>{{2}^{1-(1/\sqrt{2})}}\] holds, is
  A)
  \[\frac{5\pi }{4}\] done clear
  B)
  \[\frac{3\pi }{4}\] done clear
  C)
  \[\frac{\pi }{2}\] done clear
  D)
  All values of x done clear
  View Solution play_arrow

• question_answer99)
  If \[(1+\tan \theta )(1+\tan \varphi )=2\], then \[\theta +\varphi \]= [Karnataka CET 1993]
  A)
  \[{{30}^{o}}\] done clear
  B)
  \[{{45}^{o}}\] done clear
  C)
  \[{{60}^{o}}\] done clear
  D)
  \[{{75}^{o}}\] done clear
  View Solution play_arrow

• question_answer100)
  If \[\tan (\pi \cos \theta )=\cot (\pi \sin \theta ),\]then the value of \[\cos \left( \theta -\frac{\pi }{4} \right)\]= [UPSEAT 1999]
  A)
  \[\frac{1}{2\sqrt{2}}\] done clear
  B)
  \[\frac{1}{\sqrt{2}}\] done clear
  C)
  \[\frac{1}{3\sqrt{2}}\] done clear
  D)
  \[\frac{1}{4\sqrt{2}}\] done clear
  View Solution play_arrow

• question_answer101)
  If \[\tan (\pi \cos \theta )=\cot (\pi \sin \theta )\], then \[\sin \left( \theta +\frac{\pi }{4} \right)\] equals  [AMU 1999]
  A)
  \[\frac{1}{\sqrt{2}}\] done clear
  B)
  \[\frac{1}{2}\] done clear
  C)
  \[\frac{1}{2\sqrt{2}}\] done clear
  D)
  \[\frac{\sqrt{3}}{2}\] done clear
  View Solution play_arrow

• question_answer102)
  The value of \[\theta \]lying between 0 and \[\pi /2\]and satisfying the equation  \[\left| \,\begin{matrix}    1+{{\sin }^{2}}\theta  & {{\cos }^{2}}\theta  & 4\sin 4\theta   \\    {{\sin }^{2}}\theta  & 1+{{\cos }^{2}}\theta  & 4\sin 4\theta   \\    {{\sin }^{2}}\theta  & {{\cos }^{2}}\theta  & 1+4\sin 4\theta   \\ \end{matrix}\, \right|=0\] [IIT 1988; MNR 1992; Kurukshetra CEE 1998; DCE 1996]
  A)
  \[\frac{7\pi }{24}\] or \[\frac{11\pi }{24}\] done clear
  B)
  \[\frac{5\pi }{24}\] done clear
  C)
  \[\frac{\pi }{24}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer103)
  If cot \[(\alpha +\beta )=0,\]then \[\sin (\alpha +2\beta )=\]  [Kerala (Engg.) 2001]
  A)
  \[\sin \alpha \] done clear
  B)
  \[\cos \alpha \] done clear
  C)
  \[\sin \beta \] done clear
  D)
  \[\cos 2\beta \] done clear
  View Solution play_arrow

• question_answer104)
  If n is any integer, then the general solution of the equation \[\cos x-\sin x=\frac{1}{\sqrt{2}}\] is [J & K 2005]
  A)
  \[x=2n\pi -\frac{\pi }{12}\] or \[x=2n\pi +\frac{7\pi }{12}\] done clear
  B)
  \[x=n\pi \pm \frac{\pi }{12}\] done clear
  C)
  \[x=2n\pi +\frac{\pi }{12}\] or \[x=2n\pi -\frac{7\pi }{12}\] done clear
  D)
  \[x=n\pi +\frac{\pi }{12}\] or \[x=n\pi -\frac{7\pi }{12}\] done clear
  View Solution play_arrow

• question_answer105)
  The general solution of \[\sin x-\cos x=\sqrt{2}\], for any integer n is [Karnataka CET 2005]
  A)
  \[n\pi \] done clear
  B)
  \[2n\pi +\frac{3\pi }{4}\] done clear
  C)
  \[2n\pi \] done clear
  D)
  \[(2n+1)\,\pi \] done clear
  View Solution play_arrow

• question_answer106)
  If \[12{{\cot }^{2}}\theta -31\,\text{cosec }\theta +\text{32}=\text{0}\], then the value of \[\sin \theta \] is  [Karnataka CET 2005]
  A)
  \[\frac{3}{5}\] or 1 done clear
  B)
  \[-\sin (B+2C)=\frac{1}{2}\] or \[\frac{-2}{3}\] done clear
  C)
  \[\frac{4}{5}\] or \[\frac{3}{4}\] done clear
  D)
  \[\pm \frac{1}{2}\] done clear
  View Solution play_arrow