10th Class Mathematics Some Applications of Trigonometry Question Bank

done Trigonometry and Its Application Total Questions - 40

• question_answer1)
  If sin \[\alpha \] + cos \[\alpha \] =\[\sqrt{\mathbf{3}}\] , then the value of tan \[\alpha \] + cot \[\alpha \] is equal to_______
  A)
   1       done clear
  B)
                                  3            done clear
  C)
   \[\sqrt{3}\]     done clear
  D)
                                                         2 done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer2)
  If \[\mathbf{Sin}\,\theta -\mathbf{Cos}\,\theta \mathbf{=0,}\] then the value of  \[\mathbf{Cose}{{\mathbf{c}}^{2}}\theta -\mathbf{Se}{{\mathbf{c}}^{2}}\theta \] is equal to _________
  A)
   1                                                         done clear
  B)
   2             done clear
  C)
   \[\frac{1}{2}\]                                                              done clear
  D)
  0 done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer3)
  If PQR is an isosceles right angled triangle in which \[\angle \,PRQ=90{}^\circ ,\] then the value of \[Sec\,(R-Q)+Cos\,P\] is equal to ________
  A)
   3 Sin P        done clear
  B)
   2 Sin P        done clear
  C)
   2 Cos P                                                            done clear
  D)
  Sec P done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer4)
  If Sin (\[\alpha +\beta \]) = 1 then Cos(\[\alpha -\beta \]) can be reduced to _______
  A)
   Sin 2\[\beta \]        done clear
  B)
   Cos 2\[\beta \]        done clear
  C)
   Sin\[\alpha \]                                                                 done clear
  D)
  Cos \[\beta \] done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer5)

  Find the value of the expression given below:

  \[\frac{\mathbf{1}}{\mathbf{8}}\mathbf{cose}{{\mathbf{c}}^{\mathbf{2}}}\mathbf{(5}{{\mathbf{2}}^{\mathbf{o}}}\mathbf{-}\theta \mathbf{)-}\frac{\mathbf{1}}{\mathbf{4}}\mathbf{ta}{{\mathbf{n}}^{\mathbf{2}}}\]\[\mathbf{(3}{{\mathbf{8}}^{\mathbf{o}}}\mathbf{+}\theta \mathbf{)+}\frac{\mathbf{7}}{\mathbf{8}}\mathbf{se}{{\mathbf{c}}^{\mathbf{2}}}\mathbf{(3}{{\mathbf{8}}^{\mathbf{o}}}\mathbf{+}\theta \mathbf{)-}\frac{\mathbf{3}}{\mathbf{4}}\mathbf{co}{{\mathbf{t}}^{\mathbf{2}}}\mathbf{(5}{{\mathbf{2}}^{\mathbf{o}}}-\theta )\]

  A)
   0         done clear
  B)
                      1 done clear
  C)
   \[-\,1\]                                                              done clear
  D)
  2 done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer6)
  If cos A + \[\mathbf{co}{{\mathbf{s}}^{\mathbf{2}}}\]A = 0 then the value of the expression \[\mathbf{si}{{\mathbf{n}}^{\mathbf{2}}}\mathbf{A}\text{ }\text{ }\mathbf{si}{{\mathbf{n}}^{\mathbf{4}}}\mathbf{A}\] is _________
  A)
   0     done clear
  B)
   \[\frac{\sqrt{3}}{2}\] done clear
  C)
   \[\frac{1}{\sqrt{2}}\]                                                                 done clear
  D)
  1 done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer7)
  Which one among the following is incorrect statement for \[0{}^\circ \le \theta <90{}^\circ \]?
  A)
   The Value of tan \[\theta \] increases as \[\theta \] increases. done clear
  B)
   The Value of tan \[\theta \] increases faster than sin \[\theta \] as \[\theta \] increases. done clear
  C)
   The Value of \[\sin \theta +\cos \theta \] is always greater than 1. done clear
  D)
  The Value of \[\cos \theta \] increases as \[\theta \]  decreases.   done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer8)
  Find the value of \[\left( \frac{1-\sin \theta }{\cos \theta }+\frac{\cos \theta }{1+\sin \theta } \right)\left( \frac{1}{\cos \theta }+\tan \theta  \right)\]
  A)
   0           done clear
  B)
  1            done clear
  C)
   2         done clear
  D)
  3 done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer9)
  Simplify tan\[\frac{\mathbf{\pi }}{\mathbf{18}}\mathbf{.tan}\frac{\mathbf{\pi }}{\mathbf{9}}\mathbf{.tan}\frac{\mathbf{\pi }}{\mathbf{4}}\]\[\mathbf{.tan}\frac{\mathbf{4\pi }}{\mathbf{9}}\mathbf{.tan}\frac{\mathbf{7\pi }}{\mathbf{18}}\]
  A)
   0                                                                     done clear
  B)
   1       done clear
  C)
   2                                                                     done clear
  D)
  tan\[\frac{\pi }{3}\]             done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer10)
  If Sin 2\[\alpha \] = 2 Sin\[\alpha \] Cos \[\alpha \] and Sin \[\mathbf{40}{}^\circ \] = m, then the value of Cos\[\mathbf{8}{{\mathbf{0}}^{\mathbf{o}}}\], Cos\[\mathbf{160}{}^\circ \], is equal to
  A)
   \[\frac{1}{4}\]                                                              done clear
  B)
   \[\frac{1}{8}\]           done clear
  C)
   \[\frac{-1}{8}\]      done clear
  D)
  \[\frac{-1}{4}\] done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer11)
  Find the value of \[\mathbf{Co}{{\mathbf{s}}^{\mathbf{2}}}\mathbf{0}{}^\circ \text{ }+\text{ }\mathbf{Co}{{\mathbf{s}}^{\mathbf{2}}}\mathbf{5}{}^\circ \text{ }+\]\[\mathbf{Co}{{\mathbf{s}}^{\mathbf{2}}}\mathbf{10}{}^\circ \text{ }+\text{ }\mathbf{Co}{{\mathbf{s}}^{\mathbf{2}}}\mathbf{15}{}^\circ \text{ }+\_\_\_\_+\text{ }\mathbf{Co}{{\mathbf{s}}^{\mathbf{2}}}\mathbf{90}{}^\circ \]
  A)
   5                                                                     done clear
  B)
   7            done clear
  C)
   10                    done clear
  D)
  9 done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer12)
  The length of the shadow of a tower decreases by 30 m, when sun ray's inclination increased from\[\mathbf{45}{}^\circ \text{ }\mathbf{to}\text{ }\mathbf{60}{}^\circ \]. Find the height of the tower (in m).
  A)
   50.35                                                               done clear
  B)
   60.95         done clear
  C)
   70.95      done clear
  D)
  55 done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer13)
  Find the value of tan \[\mathbf{15{}^\circ }\] by using identity tan 2\[\theta \]= ????
  A)
   \[2+\sqrt{3}\]                                                   done clear
  B)
   \[2-\sqrt{3}\]       done clear
  C)
   \[\sqrt{3}+1\]                                                               done clear
  D)
  \[\sqrt{3}-1\] done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer14)
  \[\sqrt{-4+\sqrt{8+16{{\sec }^{4}}\theta +{{\cos }^{4}}\theta }}=\_\_\_\_\_\]
  A)
   \[\cos \theta +\tan \theta \]                                             done clear
  B)
   \[sec\theta +\cos \theta \] done clear
  C)
  \[2sec\theta -\cos \theta \]  done clear
  D)
  \[2cos\theta +\tan \theta \] done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer15)
  Identify the correct statement among the following:
  A)
   \[Sin\text{ }1{}^\circ >1\]                                            done clear
  B)
   \[Sin\text{ }1{}^\circ \text{ }>\text{ }Sin\text{ }1\] done clear
  C)
   \[Sin\text{ }1{}^\circ <\text{ }Sin\text{ }1\]     done clear
  D)
  \[Sin\text{ }1{}^\circ \text{ }=\text{ }Sin\text{ }1\] done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer16)
  If \[Co{{t}^{2}}\theta ={{a}^{2}}-1,\] then the value of Cosec \[\theta \] + \[\mathbf{Co}{{\mathbf{t}}^{\mathbf{3}}}\]\[\theta \] Sec\[\theta \] is ________
  A)
   \[{{\left( {{a}^{2}}-1 \right)}^{3/2}}\]                                                 done clear
  B)
   \[{{a}^{2}}-1\]        done clear
  C)
   \[{{a}^{3}}\]              done clear
  D)
  \[{{a}^{2}}\] done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer17)
  If m Cot \[\theta \] + n Cosec\[\theta \] = a and n Cot \[\theta \] + m Cosec\[\theta \] = b, then \[{{\mathbf{a}}^{\mathbf{2}}}-\text{ }{{\mathbf{b}}^{\mathbf{2}}}\] is equal to _______
  A)
   \[{{n}^{2}}-{{m}^{2}}\]                               done clear
  B)
   \[{{m}^{2}}+\text{ }{{n}^{2}}\]       done clear
  C)
   \[{{m}^{2}}-{{n}^{2}}\]                                                                   done clear
  D)
  \[{{\left( m-n \right)}^{2}}\] done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer18)
  In an acute angled triangle PQR, if \[\sqrt{\mathbf{2}}\] sin (P + Q - R) = 1 and tan (Q + R - P) =\[\sqrt{\mathbf{3}}\], find the values of P, Q and R.
  A)
   \[P=60{}^\circ ,\text{ }Q=52\frac{1{}^\circ }{2},\text{ }R=67\frac{1{}^\circ }{2}\]                done clear
  B)
   \[P=52\frac{1{}^\circ }{2},\text{ }Q=67\frac{1{}^\circ }{2},\text{ }R=60{}^\circ \] done clear
  C)
   \[P=37\frac{1{}^\circ }{2},\text{ }Q=90{}^\circ ,\text{ }R=52\frac{1{}^\circ }{2}\]                done clear
  D)
  \[P=90{}^\circ ,\text{ }Q=37\frac{1{}^\circ }{2},\text{ }R=52\frac{1{}^\circ }{2}\] done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer19)
  \[\frac{\tan \theta +\sec \theta -1}{\tan \theta -\sec \theta +1}=\_\_\_\_\_\]
  A)
   \[\frac{1+\sin \theta }{\cos \theta }\]                                           done clear
  B)
   \[\frac{1-\sin \theta }{\cos \theta }\]     done clear
  C)
   1+tan\[\theta \]                                                             done clear
  D)
  sec\[\theta \] + cosec\[\theta \] done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer20)
  If \[Cos\theta -Sin\,\theta =\sqrt{2}\sin \theta ,\] then \[Cos\theta +Sin\,\theta \] is equal to _____
  A)
   Cos\[\theta \]                                                                 done clear
  B)
   2 Cos\[\theta \]       done clear
  C)
   \[\sqrt{2}\]Cos\[\theta \]              done clear
  D)
  2\[\sqrt{2}\]COS\[\theta \] done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer21)
  If \[\cot \alpha +\tan \alpha =m\] and \[\sec \alpha -\cos \alpha =n,\] then \[{{\left( {{\mathbf{m}}^{\mathbf{2}}}\mathbf{n} \right)}^{\mathbf{2}/\mathbf{3}}}-\text{ }{{\left( \mathbf{m}\text{ }{{\mathbf{n}}^{\mathbf{2}}} \right)}^{\mathbf{2}/\mathbf{3}}}\]is equal to _______
  A)
   0                                                                     done clear
  B)
   1            done clear
  C)
   2                     done clear
  D)
                     sec\[\theta \]+ cos\[\theta \] done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer22)
  If \[\text{Cosec}\,\alpha -\text{Sin}\,\alpha =a\] and \[\text{Sec}\,\alpha -\text{Cos}\,\alpha =b,\]then \[\left( {{\mathbf{a}}^{\mathbf{2}}}+\text{ }{{\mathbf{b}}^{\mathbf{2}}}+\text{ }\mathbf{3} \right)\] is equal to ___­­­­­­____
  A)
   \[\frac{1}{ab}\]                                                 done clear
  B)
   \[{{a}^{2}}+{{b}^{2}}\]         done clear
  C)
   \[\frac{1}{{{a}^{2}}+{{b}^{2}}}\]        done clear
  D)
  \[{{a}^{2}}{{b}^{2}}+1\] done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer23)
  In a \[\Delta \] PQR, Sin \[\left( \frac{\mathbf{P+R}}{\mathbf{2}} \right)\] is equal to ??
  A)
   \[-\,Cos\frac{Q}{2}\]                                                                 done clear
  B)
  \[\,Cos\frac{Q}{2}\]         done clear
  C)
   \[Sin\frac{Q}{2}\]                                                                     done clear
  D)
  \[-\,Sin\frac{Q}{2}\] done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer24)
  If tan \[82{}^\circ \] = K, then \[\frac{\mathbf{tan16}{{\mathbf{4}}^{\mathbf{o}}}\mathbf{+cot}\,{{\mathbf{8}}^{\mathbf{o}}}}{\mathbf{K+cot}\,\mathbf{10}{{\mathbf{6}}^{\mathbf{o}}}}\] is equal to__________
  A)
   K                                                                     done clear
  B)
   \[{{K}^{2}}+1\]        done clear
  C)
   \[\frac{{{k}^{2}}-1}{{{k}^{2}}+1}\]                         done clear
  D)
         1 done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer25)
  If tan 18 = K then \[\frac{\mathbf{tan16}{{\mathbf{2}}^{\mathbf{o}}}\mathbf{+tan7}{{\mathbf{2}}^{\mathbf{o}}}}{\mathbf{k+tan10}{{\mathbf{8}}^{\mathbf{o}}}}\] is equal to
  A)
   \[\frac{{{k}^{2}}+1}{{{k}^{2}}-1}\]                                                             done clear
  B)
   \[\frac{{{k}^{2}}-1}{{{k}^{2}}+1}\]         done clear
  C)
   1                                                                     done clear
  D)
  \[-\,1\] done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer26)
  If\[m=k\,Sin\phi \,\,\text{Cos}\theta ,\] \[n=k\,\text{Sin}\,\phi \,\,Sin\theta \] and \[r=k\,\text{Cos}\,\phi \] then \[{{m}^{2}}+{{n}^{2}}+{{r}^{2}}=\]______
  A)
   1                                                                     done clear
  B)
   2             done clear
  C)
   \[{{k}^{2}}\]          done clear
  D)
  \[\frac{1}{{{k}^{2}}}\] done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer27)
  If \[\frac{\mathbf{sin}\,\mathbf{P}}{\mathbf{sin}\,\mathbf{Q}}\]= K and \[\frac{\mathbf{tan}\,\mathbf{P}}{\mathbf{tan}\,\mathbf{Q}}\]= I then \[\mathbf{si}{{\mathbf{n}}^{\mathbf{2}}}\]p is equal to ______
  A)
   \[\frac{{{I}^{2}}-{{k}^{2}}}{I}\]       done clear
  B)
   \[\frac{{{I}^{2}}-{{k}^{2}}}{k}\] done clear
  C)
   \[\frac{{{k}^{2}}-{{I}^{2}}}{I}\]                                                                  done clear
  D)
  \[\frac{{{k}^{2}}-1}{{{I}^{2}}-1}\] done clear
  E)
  None of these done clear
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• question_answer28)
  If \[k\,\sec \theta +I\tan \theta +m=0\] and \[x\,\sec \theta +y\,\tan \theta +z=0\] then \[{{(Iz-ym)}^{2}}-{{(xm-kz)}^{2}}=\]_____
  A)
  \[{{\left( ky\text{ }-\text{ }Ix \right)}^{2}}\]    done clear
  B)
   \[{{\left( kx\text{ }-\text{ }Iy \right)}^{2}}\] done clear
  C)
   \[{{\left( Ix\text{ }+ky \right)}^{2}}\]                                                    done clear
  D)
  \[{{\left( kz\text{ }-\text{ }Ix \right)}^{2}}\] done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer29)
  A spherical balloon of radius 3cm subtends an angle of \[60{}^\circ \] at the eye of the observer. If the angle of elevation of its centre is \[45{}^\circ \], then the height of the centre of the balloon is __
  A)
   6\[\sqrt{2}\] cm                                                 done clear
  B)
   3\[\sqrt{2}\] cm     done clear
  C)
   9cm                                                                 done clear
  D)
  3cm done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer30)
  If p Cos\[\theta \] - q Sin\[\theta \] = \[\sqrt{{{\mathbf{p}}^{\mathbf{2}}}\mathbf{+}{{\mathbf{q}}^{\mathbf{2}}}\mathbf{-}{{\mathbf{r}}^{\mathbf{2}}}}\] then the value of \[p\,Sin\theta +q\,Cos\theta \] is equal to
  A)
   \[\sqrt{{{p}^{2}}+{{q}^{2}}+{{r}^{2}}}\]                                                 done clear
  B)
   \[\sqrt{{{p}^{2}}-{{q}^{2}}+{{r}^{2}}}\] done clear
  C)
   \[\sqrt{{{p}^{2}}+{{q}^{2}}}\]      done clear
  D)
   r done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer31)
  The angle of elevation of a jet plane from a point Q on the ground is\[\mathbf{60{}^\circ }\]. After a flight of 20 seconds, the angle of elevation changes to\[\mathbf{45{}^\circ }\]. If the Jet plane is flying at a constant height of 3000\[\sqrt{\mathbf{3}}\] m, then find the speed of the jet plane.
  A)
   295.18 km/hr                                                    done clear
  B)
   395.28 km/hr done clear
  C)
   255.20 km/hr                                        done clear
  D)
  345.38 km/hr done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer32)
  The angle of elevation of a cloud from a point 90m above a lake is \[\mathbf{30}{}^\circ \] and the angle of depression of the reflection of cloud in the lake is\[\mathbf{60}{}^\circ \]. Find the height of the cloud.
  A)
   90m                                                                 done clear
  B)
   120m done clear
  C)
   180m         done clear
  D)
  45m done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer33)
  The angle of elevation of a cliff from a fixed point is\[\mathbf{45{}^\circ }\]. On up a distance of 300 m towards the top of the cliff at an angle of \[\mathbf{30{}^\circ }\], it is that the angle of elevation is\[\mathbf{60{}^\circ }.\] The height of the cliff is ________
  A)
   93.42 m                                                           done clear
  B)
   97.12 m done clear
  C)
   102.18 m                                                          done clear
  D)
  112.39 m done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer34)
  A ladder rests against a wall at an angle \[\theta \] to the horizontal. Its foot is away from the wall through a distance ?m?, so that it slides a distance 'n' down the wall making an angle\[\phi \]with the horizontal then \[\frac{\mathbf{n}}{\mathbf{m}}\] is equal to _________
  A)
   \[\frac{\cos \theta -\cos \phi }{\sin \phi -\sin \theta }\]                                             done clear
  B)
   \[\frac{\sin \phi -\sin \theta }{\cos \theta -\cos \phi }\] done clear
  C)
   \[\frac{\cos \theta +\cos \phi }{\sin \phi +\sin \theta }\]                                                     done clear
  D)
  \[\frac{\sin \phi +\sin \theta }{\cos \theta +\cos \phi }\] done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer35)
  If 15 Sin A + 8 Cos A = 8 then find the value of 8 Sin A - 15 Cos A.
  A)
   8                                                                     done clear
  B)
   12 done clear
  C)
   15            done clear
  D)
  64 done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer36)
  The lower window of a house is at a height of 3 m above the ground and its upper window is 5m vertically above the lower window. At certain instant it is found that the angles of elevation of a balloon from these windows are \[\mathbf{60}{}^\circ \] and \[\mathbf{30}{}^\circ \]respectively. Find the height of the balloon above the ground.
  A)
   8.5 m                                                               done clear
  B)
   10.5 m done clear
  C)
   7.5 m                                                               done clear
  D)
  8 m done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer37)
  Simplify Sin12 \[\theta \]- \[\mathbf{Co}{{\mathbf{s}}^{\mathbf{12}}}\] \[\theta \].
  A)
   \[Cos2~\theta (1-Si{{n}^{2}}\theta ~Co{{s}^{2}}\theta )\text{ }(1-3Si{{n}^{2}}\theta ~Co{{s}^{2}}\theta )\] done clear
  B)
    \[Co{{s}^{2}}\theta ~(1-Si{{n}^{2}}\theta ~Co{{s}^{2}}\theta )\text{ }(1-2\text{ }Si{{n}^{2}}\theta ~Co{{s}^{2}}\theta )\] done clear
  C)
   \[Cos2\theta (1-2\text{ }Si{{n}^{2}}\theta Co{{s}^{2}}\theta )(1-3\text{ }Si{{n}^{2}}\theta ~Co{{s}^{2}}\theta )\] done clear
  D)
   \[Si{{n}^{2}}\theta (1-2\text{ }Si{{n}^{2}}\theta Co{{s}^{2}}\theta )\text{ }(1-3\text{ }Si{{n}^{2}}\theta Co{{s}^{2}}\theta )\] done clear
  E)
   None of these done clear
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• question_answer38)
  If \[4\sqrt{2}\,\text{Sin}\,\theta -2\sqrt{6}\,Cos\,\theta =\sqrt{6}\] then value of \[\theta \] can be ________
  A)
  \[0{}^\circ \]                                                                done clear
  B)
   \[30{}^\circ \] done clear
  C)
  \[45{}^\circ \]                                                               done clear
  D)
  \[60{}^\circ \] done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer39)
  If cosec\[\theta \] + cot\[\theta \] = 2 where \[\mathbf{0{}^\circ <}\theta \mathbf{< 90{}^\circ }\] then the value of tan\[\theta \] + sec\[\theta \] is equal to _________
  A)
   0    done clear
  B)
                                                                      1 done clear
  C)
   2                                                                     done clear
  D)
  3 done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer40)
  The angle of elevation of the top of a tower from a point A due south of the tower is and from a point B due east of the tower is\[\mathbf{45}{}^\circ .\] If AB = 160 metre then the height of the tower is _________
  A)
   \[\frac{160}{\sqrt{3}}\] m                      done clear
  B)
          75\[\sqrt{3}\] m done clear
  C)
   80\[\sqrt{3}\] m                                                             done clear
  D)
  80 m done clear
  E)
  None of these done clear
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