JEE Main & Advanced Mathematics Trigonometric Identities Question Bank

done Trigonometrical ratios of multiple and sub multiple angles Total Questions - 66

• question_answer1)
  \[\frac{{{\cot }^{2}}15{}^\circ -1}{{{\cot }^{2}}15{}^\circ +1}=\] [MP PET 1998]
  A)
  \[\frac{1}{2}\] done clear
  B)
  \[\frac{\sqrt{3}}{2}\] done clear
  C)
  \[\frac{3\sqrt{3}}{4}\] done clear
  D)
  \[\sqrt{3}\] done clear
  View Solution play_arrow

• question_answer2)
  If \[\cos \theta =\frac{3}{5}\]and \[\cos \varphi =\frac{4}{5},\]where \[\theta \]and \[\varphi \]are positive acute angles, then \[\cos \frac{\theta -\varphi }{2}=\] [MP PET 1988]
  A)
  \[\frac{7}{\sqrt{2}}\] done clear
  B)
  \[\frac{7}{5\sqrt{2}}\] done clear
  C)
  \[\frac{7}{\sqrt{5}}\] done clear
  D)
  \[\frac{7}{2\sqrt{5}}\] done clear
  View Solution play_arrow

• question_answer3)
  If \[\sec \theta =1\frac{1}{4}\], then \[\tan \frac{\theta }{2}=\]
  A)
  \[\frac{1}{3}\] done clear
  B)
  \[\frac{3}{4}\] done clear
  C)
  \[\frac{1}{4}\] done clear
  D)
  \[\frac{5}{4}\] done clear
  View Solution play_arrow

• question_answer4)
  If \[\tan \frac{A}{2}=\frac{3}{2},\]then \[\frac{1+\cos A}{1-\cos A}=\]
  A)
  \[-5\] done clear
  B)
  \[5\] done clear
  C)
  \[9/4\] done clear
  D)
  \[4/9\] done clear
  View Solution play_arrow

• question_answer5)
  If \[\cos A=\frac{\sqrt{3}}{2},\]then \[\tan 3A=\]
  A)
  \[0\] done clear
  B)
  \[1/2\] done clear
  C)
  \[1\] done clear
  D)
  \[\infty \] done clear
  View Solution play_arrow

• question_answer6)
  \[\sin 4\theta \]can be written as
  A)
  \[4\sin \theta (1-2{{\sin }^{2}}\theta )\sqrt{1-{{\sin }^{2}}\theta }\] done clear
  B)
  \[2\sin \theta \cos \theta {{\sin }^{2}}\theta \] done clear
  C)
  \[4\sin \theta -6{{\sin }^{3}}\theta \] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer7)
  If \[\cos 2B=\frac{\cos (A+C)}{\cos (A-C)}\], then \[\tan A,\ \tan B,\ \tan C\] are in
  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_answer8)
  If \[a\tan \theta =b\], then \[a\cos 2\theta +b\sin 2\theta =\] [EAMCET 1981, 82; MP PET 1996; J & K 2005]
  A)
  \[a\] done clear
  B)
  \[b\] done clear
  C)
  \[-a\] done clear
  D)
  \[-b\] done clear
  View Solution play_arrow

• question_answer9)
  \[\frac{\sin 2A}{1+\cos 2A}.\frac{\cos A}{1+\cos A}=\]
  A)
  \[\tan \frac{A}{2}\] done clear
  B)
  \[\cot \frac{A}{2}\] done clear
  C)
  \[\sec \frac{A}{2}\] done clear
  D)
  \[\text{cosec}\frac{A}{2}\] done clear
  View Solution play_arrow

• question_answer10)
  \[\frac{1}{\tan 3A-\tan A}-\frac{1}{\cot 3A-\cot A}=\]
  A)
  \[\tan A\] done clear
  B)
  \[\tan 2A\] done clear
  C)
  \[\cot A\] done clear
  D)
  \[\cot 2A\] done clear
  View Solution play_arrow

• question_answer11)
  \[\text{cosec }A-2\cot 2A\cos A=\]
  A)
  \[2\sin A\] done clear
  B)
  \[\sec A\] done clear
  C)
  \[2\cos A\cot A\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer12)
  \[\sqrt{2+\sqrt{2+2\cos 4\theta }}=\]
  A)
  \[\cos \theta \] done clear
  B)
  \[\sin \theta \] done clear
  C)
  \[2\cos \theta \] done clear
  D)
  \[2\sin \theta \] done clear
  View Solution play_arrow

• question_answer13)
  If \[\cos 3\theta =\alpha \cos \theta +\beta {{\cos }^{3}}\theta ,\]then \[(\alpha ,\beta )=\]
  A)
  \[(3,\,4)\] done clear
  B)
  \[(4,\,3)\] done clear
  C)
  \[(-3,\,4)\] done clear
  D)
  \[(3,\,-4)\] done clear
  View Solution play_arrow

• question_answer14)
  \[{{(\cos \alpha +\cos \beta )}^{2}}+{{(\sin \alpha +\sin \beta )}^{2}}=\]
  A)
  \[4{{\cos }^{2}}\frac{\alpha -\beta }{2}\] done clear
  B)
  \[4{{\sin }^{2}}\frac{\alpha -\beta }{2}\] done clear
  C)
  \[4{{\cos }^{2}}\frac{\alpha +\beta }{2}\] done clear
  D)
  \[4{{\sin }^{2}}\frac{\alpha +\beta }{2}\] done clear
  View Solution play_arrow

• question_answer15)
  If \[\tan x=\frac{b}{a},\]then \[\sqrt{\frac{a+b}{a-b}}+\sqrt{\frac{a-b}{a+b}}=\] [MP PET 1990, 2002]
  A)
  \[\frac{2\sin x}{\sqrt{\sin 2x}}\] done clear
  B)
  \[\frac{2\cos x}{\sqrt{\cos 2x}}\] done clear
  C)
  \[\frac{2\cos x}{\sqrt{\sin 2x}}\] done clear
  D)
  \[\frac{2\sin x}{\sqrt{\cos 2x}}\] done clear
  View Solution play_arrow

• question_answer16)
  \[1-2{{\sin }^{2}}\left( \frac{\pi }{4}+\theta  \right)=\]
  A)
  \[\cos 2\theta \] done clear
  B)
  \[-\cos 2\theta \] done clear
  C)
  \[\sin 2\theta \] done clear
  D)
  \[-\sin 2\theta \] done clear
  View Solution play_arrow

• question_answer17)
  \[\frac{\sin 3A-\cos \left( \frac{\pi }{2}-A \right)}{\cos A+\cos (\pi +3A)}=\]
  A)
  \[\tan A\] done clear
  B)
  \[\cot A\] done clear
  C)
  \[\tan 2A\] done clear
  D)
  \[\cot 2A\] done clear
  View Solution play_arrow

• question_answer18)
  If \[\tan A=\frac{1}{2},\]then \[\tan 3A=\]
  A)
  \[\frac{9}{2}\] done clear
  B)
  \[\frac{11}{2}\] done clear
  C)
  \[\frac{7}{2}\] done clear
  D)
  \[-\frac{1}{2}\] done clear
  View Solution play_arrow

• question_answer19)
  \[\frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}}=\] (when x lies in IInd quadrant)
  A)
  \[\sin \frac{x}{2}\] done clear
  B)
  \[\tan \frac{x}{2}\] done clear
  C)
  \[\sec \frac{x}{2}\] done clear
  D)
  \[\text{cosec}\frac{x}{2}\] done clear
  View Solution play_arrow

• question_answer20)
  \[(\sec 2A+1){{\sec }^{2}}A=\]
  A)
  \[\sec A\] done clear
  B)
  \[2\sec A\] done clear
  C)
  \[\sec 2A\] done clear
  D)
  \[2\sec 2A\] done clear
  View Solution play_arrow

• question_answer21)
  \[2\sin A{{\cos }^{3}}A-2{{\sin }^{3}}A\cos A=\] [Roorkee 1975; Kerala (Engg.) 2001]
  A)
  \[\sin 4A\] done clear
  B)
  \[\frac{1}{2}\sin 4A\] done clear
  C)
  \[\frac{1}{4}\sin 4A\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer22)
  \[\frac{\sin \theta +\sin 2\theta }{1+\cos \theta +\cos 2\theta }=\] [Roorkee 1971]
  A)
  \[\frac{1}{2}\tan \theta \] done clear
  B)
  \[\frac{1}{2}\cot \theta \] done clear
  C)
  \[\tan \theta \] done clear
  D)
  \[\cot \theta \] done clear
  View Solution play_arrow

• question_answer23)
  If\[\frac{2\sin \alpha }{\{1+\cos \alpha +\sin \alpha \}}=y,\]then \[\frac{\{1-\cos \alpha +\sin \alpha \}}{1+\sin \alpha }=\] [BIT Ranchi 1996; Orissa JEE 2004]
  A)
  \[\frac{1}{y}\] done clear
  B)
  \[y\] done clear
  C)
  \[1-y\] done clear
  D)
  \[1+y\] done clear
  View Solution play_arrow

• question_answer24)
  If \[\tan \alpha =\frac{1}{7}\]and \[\sin \beta =\frac{1}{\sqrt{10}}\left( 0<\alpha ,\,\beta <\frac{\pi }{2} \right)\], then \[2\beta \]is equal to
  A)
  \[\frac{\pi }{4}-\alpha \] done clear
  B)
  \[\frac{3\pi }{4}-\alpha \] done clear
  C)
  \[\frac{\pi }{8}-\frac{\alpha }{2}\] done clear
  D)
  \[\frac{3\pi }{8}-\frac{\alpha }{2}\] done clear
  View Solution play_arrow

• question_answer25)
  If \[\cos (\theta -\alpha ),\ \cos \theta \]and \[\cos (\theta +\alpha )\]are in H.P., then \[\cos \theta \sec \frac{\alpha }{2}\]is equal to [IIT 1997]
  A)
  \[\pm \sqrt{2}\] done clear
  B)
  \[\pm \sqrt{3}\] done clear
  C)
  \[\pm 1/\sqrt{2}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer26)
  If \[\sin \theta +\sin \varphi =a\]and \[\cos \theta +\cos \varphi =b,\]then \[\tan \frac{\theta -\varphi }{2}\]is equal to [MP PET 1993]
  A)
  \[\sqrt{\frac{{{a}^{2}}+{{b}^{2}}}{4-{{a}^{2}}-{{b}^{2}}}}\] done clear
  B)
  \[\sqrt{\frac{4-{{a}^{2}}-{{b}^{2}}}{{{a}^{2}}+{{b}^{2}}}}\] done clear
  C)
  \[\sqrt{\frac{{{a}^{2}}+{{b}^{2}}}{4+{{a}^{2}}+{{b}^{2}}}}\] done clear
  D)
  \[\sqrt{\frac{4+{{a}^{2}}+{{b}^{2}}}{{{a}^{2}}+{{b}^{2}}}}\] done clear
  View Solution play_arrow

• question_answer27)
  If \[\tan A=\frac{1-\cos B}{\sin B},\]find\[\tan 2A\]in terms of \[\tan B\]and show that [IIT 1983; MP PET 1994]
  A)
  \[\tan 2A=\tan B\] done clear
  B)
  \[\tan 2A={{\tan }^{2}}B\] done clear
  C)
  \[\tan 2A={{\tan }^{2}}B+2\tan B\] done clear
  D)
  None of the above done clear
  View Solution play_arrow

• question_answer28)
  If \[\sin \beta \]is the geometric mean between \[\sin \alpha \]and \[\cos \alpha ,\]then \[\cos 2\beta \]is equal to
  A)
  \[2{{\sin }^{2}}\left( \frac{\pi }{4}-\alpha  \right)\] done clear
  B)
  \[2{{\cos }^{2}}\left( \frac{\pi }{4}-\alpha  \right)\] done clear
  C)
  \[2{{\cos }^{2}}\left( \frac{\pi }{4}+\alpha  \right)\] done clear
  D)
  \[2{{\sin }^{2}}\left( \frac{\pi }{4}+\alpha  \right)\] done clear
  View Solution play_arrow

• question_answer29)
  \[\frac{\sec 8A-1}{\sec 4A-1}=\] [MP PET 1995]
  A)
  \[\frac{\tan 2A}{\tan 8A}\] done clear
  B)
  \[\frac{\tan 8A}{\tan 2A}\] done clear
  C)
  \[\frac{\cot 8A}{\cot 2A}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer30)
  If \[\frac{\cos A}{\sin B\sin C}+\frac{\cos B}{\sin C\sin A}+\frac{\cos C}{\sin A\sin B}=\]then \[32\sin \left( \frac{A}{2} \right)\sin \left( \frac{5A}{2} \right)=\] [DCE 1996]
  A)
  7 done clear
  B)
  8 done clear
  C)
  11 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer31)
  \[\tan 15{}^\circ =\] [EAMCET 1981]
  A)
  \[\frac{1}{3}\] done clear
  B)
  \[\sqrt{3}-2\] done clear
  C)
  \[2-\sqrt{3}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer32)
  If \[\tan \alpha =\frac{1}{7},\ \tan \beta =\frac{1}{3},\]then \[\cos 2\alpha =\] [CET 1986]
  A)
  \[\sin 2\beta \] done clear
  B)
  \[\sin 4\beta \] done clear
  C)
  \[\sin 3\beta \] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer33)
  If \[\tan \beta =\cos \theta \tan \alpha ,\]then \[{{\tan }^{2}}\frac{\theta }{2}=\]
  A)
  \[\frac{\sin (\alpha +\beta )}{\sin (\alpha -\beta )}\] done clear
  B)
  \[\frac{\cos (\alpha -\beta )}{\cos (\alpha +\beta )}\] done clear
  C)
  \[\frac{\sin (\alpha -\beta )}{\sin (\alpha +\beta )}\] done clear
  D)
  \[\frac{\cos (\alpha +\beta )}{\cos (\alpha -\beta )}\] done clear
  View Solution play_arrow

• question_answer34)
  .If \[\cos A=\frac{3}{4}\], then \[32\sin \frac{A}{2}\cos \frac{5}{2}A=\] [EAMCET 1982]
  A)
  \[\sqrt{7}\] done clear
  B)
  \[-\sqrt{7}\] done clear
  C)
  7 done clear
  D)
  -7 done clear
  View Solution play_arrow

• question_answer35)
  If \[\theta \]and \[\varphi \]are angles in the 1st quadrant such that \[\tan \theta =1/7\]and \[\sin \varphi =1/\sqrt{10}\].Then [Kurukshetra CEE 1998; AMU 2001]
  A)
  \[\theta +2\varphi =90{}^\circ \] done clear
  B)
  \[\theta +2\varphi =60{}^\circ \] done clear
  C)
  \[\theta +2\varphi =30{}^\circ \] done clear
  D)
  \[\theta +2\varphi =45{}^\circ \] done clear
  View Solution play_arrow

• question_answer36)
  \[\frac{\cos A}{1-\sin A}=\]
  A)
  \[\sec A-\tan A\] done clear
  B)
  \[\text{cosec}\,A+\cot A\] done clear
  C)
  \[\tan \left( \frac{\pi }{4}-\frac{A}{2} \right)\] done clear
  D)
  \[\tan \left( \frac{\pi }{4}+\frac{A}{2} \right)\] done clear
  View Solution play_arrow

• question_answer37)
  \[\tan \frac{A}{2}\]is equal to
  A)
  \[\pm \sqrt{\frac{1-\sin A}{1+\sin A}}\] done clear
  B)
  \[\pm \sqrt{\frac{1+\sin A}{1-\sin A}}\] done clear
  C)
  \[\pm \sqrt{\frac{1-\cos A}{1+\cos A}}\] done clear
  D)
  \[\pm \sqrt{\frac{1+\cos A}{1-\cos A}}\] done clear
  View Solution play_arrow

• question_answer38)
  If \[\sin \alpha =\frac{-3}{5},\]where \[\pi <\alpha <\frac{3\pi }{2},\]then \[\cos \frac{1}{2}\alpha =\] [MP PET 1998]
  A)
  \[\frac{-1}{\sqrt{10}}\] done clear
  B)
  \[\frac{1}{\sqrt{10}}\] done clear
  C)
  \[\frac{3}{\sqrt{10}}\] done clear
  D)
  \[\frac{-3}{\sqrt{10}}\] done clear
  View Solution play_arrow

• question_answer39)
  Let\[0<x<\frac{\pi }{4}.\]Then \[\sec 2x-\tan 2x=\] [IIT Screening 1994]
  A)
  \[\tan \left( x-\frac{\pi }{4} \right)\] done clear
  B)
  \[\tan \left( \frac{\pi }{4}-x \right)\] done clear
  C)
  \[\tan \left( x+\frac{\pi }{4} \right)\] done clear
  D)
  \[{{\tan }^{2}}\left( x+\frac{\pi }{4} \right)\] done clear
  View Solution play_arrow

• question_answer40)
  If \[\sin \theta +\cos \theta =x,\] then \[{{\sin }^{6}}\theta +{{\cos }^{6}}\theta =\frac{1}{4}[4-3{{({{x}^{2}}-1)}^{2}}]\] for
  A)
  All real x done clear
  B)
  \[{{x}^{2}}\le 2\] done clear
  C)
  \[{{x}^{2}}\ge 2\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer41)
  If \[\tan \theta =t,\]then \[\tan 2\theta +\sec 2\theta =\] [MP PET 1999]
  A)
  \[\frac{1+t}{1-t}\] done clear
  B)
  \[\frac{1-t}{1+t}\] done clear
  C)
  \[\frac{2t}{1-t}\] done clear
  D)
  \[\frac{2t}{1+t}\] done clear
  View Solution play_arrow

• question_answer42)
  \[\frac{\sqrt{2}-\sin \alpha -\cos \alpha }{\sin \alpha -\cos \alpha }=\] [AMU 1999]
  A)
  \[\sec \left( \frac{\alpha }{2}-\frac{\pi }{8} \right)\] done clear
  B)
  \[\cos \left( \frac{\pi }{8}-\frac{\alpha }{2} \right)\] done clear
  C)
  \[\tan \left( \frac{\alpha }{2}-\frac{\pi }{8} \right)\] done clear
  D)
  \[\cot \left( \frac{\alpha }{2}-\frac{\pi }{2} \right)\] done clear
  View Solution play_arrow

• question_answer43)
  If \[\cos \theta =\frac{1}{2}\left( a+\frac{1}{a} \right),\]then the value of \[\cos 3\theta \]is [MP PET 2001; Pb. CET 2002]
  A)
  \[\frac{1}{8}\left( {{a}^{3}}+\frac{1}{{{a}^{3}}} \right)\] done clear
  B)
  \[\frac{3}{2}\left( a+\frac{1}{a} \right)\] done clear
  C)
  \[\frac{1}{2}\left( {{a}^{3}}+\frac{1}{{{a}^{3}}} \right)\] done clear
  D)
  \[\frac{1}{3}\left( {{a}^{3}}+\frac{1}{{{a}^{3}}} \right)\] done clear
  View Solution play_arrow

• question_answer44)
  If \[\alpha \] is a root of \[25{{\cos }^{2}}\theta +5\cos \theta -12=0\], \[\pi /2<\alpha <\pi \], then \[\sin 2\alpha \]is equal to [UPSEAT 2001]
  A)
  \[24/25\] done clear
  B)
  \[-24/25\] done clear
  C)
  \[13/18\] done clear
  D)
  \[-13/18\] done clear
  View Solution play_arrow

• question_answer45)
  For \[A=133{}^\circ ,\ 2\cos \frac{A}{2}\]is equal to [DCE 2001]
  A)
  \[-\sqrt{1+\sin A}-\sqrt{1-\sin A}\] done clear
  B)
    \[-\sqrt{1+\sin A}+\sqrt{1-\sin A}\] done clear
  C)
  \[\sqrt{1+\sin A}-\sqrt{1-\sin A}\] done clear
  D)
  \[\sqrt{1+\sin A}+\sqrt{1-\sin A}\] done clear
  View Solution play_arrow

• question_answer46)
  If \[90{}^\circ <A<180{}^\circ \]and \[\sin A=\frac{4}{5},\]then \[\tan \frac{A}{2}\]is equal to [AMU 2001]
  A)
  \[1/2\] done clear
  B)
  \[3/5\] done clear
  C)
  \[3/2\] done clear
  D)
  \[2\] done clear
  View Solution play_arrow

• question_answer47)
  If \[2\tan A=3\tan B,\]then \[\frac{\sin 2B}{5-\cos 2B}\]is equal to [AMU 2001]
  A)
  \[\tan A-\tan B\] done clear
  B)
  \[\tan (A-B)\] done clear
  C)
  \[\tan (A+B)\] done clear
  D)
  \[\tan (A+2B)\] done clear
  View Solution play_arrow

• question_answer48)
  . Given that \[\cos \left( \frac{\alpha -\beta }{2} \right)=2\cos \left( \frac{\alpha +B}{2} \right)\], then \[\tan \frac{\alpha }{2}\tan \frac{\beta }{2}\]is equal to [AMU 2001]
  A)
  \[\frac{1}{2}\] done clear
  B)
  \[\frac{1}{3}\] done clear
  C)
  \[\frac{1}{4}\] done clear
  D)
  \[\frac{1}{8}\] done clear
  View Solution play_arrow

• question_answer49)
  If \[\tan \frac{\theta }{2}=t,\]then \[\frac{1-{{t}^{2}}}{1+{{t}^{2}}}\]is equal to [Kerala (Engg.) 2002]
  A)
  \[\cos \theta \] done clear
  B)
  \[\sin \theta \] done clear
  C)
  \[\sec \theta \] done clear
  D)
  \[\cos 2\theta \] done clear
  View Solution play_arrow

• question_answer50)
  If \[\sqrt{x}+\frac{1}{\sqrt{x}}=2\cos \theta ,\]then \[{{x}^{6}}+{{x}^{-6}}=\] [Karnataka CET 2003]
  A)
  \[2\cos 6\theta \] done clear
  B)
  \[2\cos 12\theta \] done clear
  C)
  \[2\cos 3\theta \] done clear
  D)
  \[2\sin 3\theta \] done clear
  View Solution play_arrow

• question_answer51)
  If \[\sin 2\theta +\sin 2\varphi =1/2\] and \[\cos 2\theta +\cos 2\varphi =3/2\], then \[{{\cos }^{2}}(\theta -\varphi )=\] [MP PET 2000; Pb. CET 2000]
  A)
  \[3/8\] done clear
  B)
  \[A+B+C=\pi ,\] done clear
  C)
  \[3/4\] done clear
  D)
  \[5/4\] done clear
  View Solution play_arrow

• question_answer52)
  \[\cos 2(\theta +\varphi )-4\cos (\theta +\varphi )\sin \theta \sin \varphi +2{{\sin }^{2}}\varphi =\] [Orissa JEE 2004]
  A)
  \[\cos 2\theta \] done clear
  B)
  \[\cos 3\theta \] done clear
  C)
  \[\sin 2\theta \] done clear
  D)
  \[\sin 3\theta \] done clear
  View Solution play_arrow

• question_answer53)
  Which of the following number(s) is/are rational [IIT 1998]
  A)
  \[\sin 15{}^\circ \] done clear
  B)
  \[\cos 15{}^\circ \] done clear
  C)
  \[\sin 15{}^\circ \cos 15{}^\circ \] done clear
  D)
  \[\sin 15{}^\circ \cos 75{}^\circ \] done clear
  View Solution play_arrow

• question_answer54)
  \[\cos 15{}^\circ =\] [MP PET 1988; MNR 1978]
  A)
  \[\sqrt{\frac{1+\cos 30{}^\circ }{2}}\] done clear
  B)
  \[\sqrt{\frac{1-\cos 30{}^\circ }{2}}\] done clear
  C)
  \[\pm \sqrt{\frac{1+\cos 30{}^\circ }{2}}\] done clear
  D)
  \[\pm \sqrt{\frac{1-\cos 30{}^\circ }{2}}\] done clear
  View Solution play_arrow

• question_answer55)
  If \[\sin A+\cos A=\sqrt{2},\]then \[{{\cos }^{2}}A=\]
  A)
  \[\frac{1}{4}\] done clear
  B)
  \[\frac{1}{2}\] done clear
  C)
  \[\frac{1}{\sqrt{2}}\] done clear
  D)
  \[\frac{3}{2}\] done clear
  View Solution play_arrow

• question_answer56)
  \[2{{\cos }^{2}}\theta -2{{\sin }^{2}}\theta =1\],then \[\theta \]= [Karnataka CET 1998]
  A)
  \[15{}^\circ \] done clear
  B)
  \[30{}^\circ \] done clear
  C)
  \[45{}^\circ \] done clear
  D)
  \[60{}^\circ \] done clear
  View Solution play_arrow

• question_answer57)
  If \[\sin \alpha =\frac{336}{625}\]and \[450{}^\circ <\alpha <540{}^\circ ,\] then \[\sin \left( \frac{\alpha }{4} \right)=\]
  A)
  \[\frac{1}{5\sqrt{2}}\] done clear
  B)
  \[\frac{7}{25}\] done clear
  C)
  \[\frac{4}{5}\] done clear
  D)
  \[\frac{3}{5}\] done clear
  View Solution play_arrow

• question_answer58)
  If \[{{\tan }^{2}}\theta =2{{\tan }^{2}}\varphi +1,\] then \[\cos 2\theta +{{\sin }^{2}}\varphi \] equals
  A)
  -1 done clear
  B)
  0 done clear
  C)
  1 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer59)
  \[{{\cos }^{4}}\frac{\pi }{8}+{{\cos }^{4}}\frac{3\pi }{8}+{{\cos }^{4}}\frac{5\pi }{8}+{{\cos }^{4}}\frac{7\pi }{8}=\]
  A)
  \[\frac{1}{2}\] done clear
  B)
  \[\frac{1}{4}\] done clear
  C)
  \[\frac{3}{2}\] done clear
  D)
  \[\frac{3}{4}\] done clear
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• question_answer60)
  If \[\sin x+\cos x=\frac{1}{5},\]then \[\tan 2x\]is [UPSEAT 2003]
  A)
  \[\frac{25}{17}\] done clear
  B)
  \[\frac{7}{25}\] done clear
  C)
  \[\frac{25}{7}\] done clear
  D)
  \[\frac{24}{7}\] done clear
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• question_answer61)
  \[{{\cos }^{2}}A{{(3-4{{\cos }^{2}}A)}^{2}}+{{\sin }^{2}}A{{(3-4{{\sin }^{2}}A)}^{2}}=\]
  A)
  \[\cos 4A\] done clear
  B)
  \[\sin 4A\] done clear
  C)
  1 done clear
  D)
  None of these done clear
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• question_answer62)
  \[\frac{\tan A+\sec A-1}{\tan A-\sec A+1}=\]
  A)
  \[\frac{1-\sin A}{\cos A}\] done clear
  B)
  \[\frac{1-\cos A}{\sin A}\] done clear
  C)
  \[\frac{1+\sin A}{\cos A}\] done clear
  D)
  \[\frac{1+\cos A}{\sin A}\] done clear
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• question_answer63)
  \[\sqrt{\frac{1-\sin A}{1+\sin A}}=\]
  A)
  \[\sec A+\tan A\] done clear
  B)
  \[\tan \left( \frac{\pi }{4}-A \right)\] done clear
  C)
  \[\tan \left( \frac{\pi }{4}+\frac{A}{2} \right)\] done clear
  D)
  \[\tan \left( \frac{\pi }{4}-\frac{A}{2} \right)\] done clear
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• question_answer64)
  \[\frac{\sin 3\theta -\cos 3\theta }{\sin \theta +\cos \theta }+1=\]
  A)
  \[2\sin 2\theta \] done clear
  B)
  \[2\cos 2\theta \] done clear
  C)
  \[\tan 2\theta \] done clear
  D)
  \[\cot 2\theta \] done clear
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• question_answer65)
  The value of \[\tan 7\frac{1}{2}{}^\circ \] is equal to [J & K 2005]
  A)
  \[\sqrt{6}+\sqrt{3}+\sqrt{2}-2\] done clear
  B)
  \[\sqrt{6}-\sqrt{3}+\sqrt{2}-2\] done clear
  C)
  \[\sqrt{6}-\sqrt{3}+\sqrt{2}+2\] done clear
  D)
  \[\sqrt{6}-\sqrt{3}-\sqrt{2}-2\] done clear
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• question_answer66)
  If \[\theta \]is an acute angle and \[\sin \frac{\theta }{2}=\sqrt{\frac{x-1}{2x}}\], then \[\tan \theta \] is equal to [Orissa  JEE 2005]
  A)
  \[{{x}^{2}}-1\] done clear
  B)
  \[\sqrt{{{x}^{2}}-1}\] done clear
  C)
  \[\sqrt{{{x}^{2}}+1}\] done clear
  D)
  \[{{x}^{2}}+1\] done clear
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