CBSE Questions for Class 10 Maths Introduction To Trigonometry Quiz 8 - MCQExams.com

The value of $$\displaystyle \frac { 2\cos { { 67 }^{ o } }  }{ \sin { { 23 }^{ o } }  } -\frac { \tan { { 40 }^{ o } }  }{ \cot { { 50 }^{ o } }  } -\sin { { 90 }^{ o } } $$ is :
  • 1
  • 0
  • 2
  • 4
The value of   $$\displaystyle \sin { \theta  } \cos { \theta  } -\frac { \sin { \theta  } \cos { \left( { 90 }^{ o }-\theta  \right)  } \cos { \theta  }  }{ \sec { \left( { 90 }^{ o }-\theta  \right)  }  } -\frac { \cos { \theta  } \sin { \left( { 90 }^{ o }-\theta  \right)  } \sin { \theta  }  }{ \text{cosec }\left( { 90 }^{ o }-\theta  \right)  } $$ is :
  • $$-1$$
  • $$2$$
  • $$-2$$
  • $$0$$
If $$\displaystyle \sec 2A=\text{cosec } \left ( A-42^{\circ} \right )$$ where $$2A$$ is acute angle, then value of $$A$$ is
  • $$\displaystyle 44^{\circ}$$
  • $$\displaystyle 22^{\circ}$$
  • $$\displaystyle 21^{\circ}$$
  • $$\displaystyle 66^{\circ}$$
Find the value of $$4\cos^2{60^0}+4\tan^2{45^0}-cosec^2\ {30^0}$$
  • $$0$$
  • $$2$$
  • $$1$$
  • $$\displaystyle\frac{1}{2}$$
If  $$\displaystyle \sin \theta =\dfrac12$$ and  $$\displaystyle 0^{\circ}< \theta < 90^{\circ} $$ then  $$\displaystyle \cos 2\theta =$$ _____
  • $$0$$
  • $$1$$
  • $$\displaystyle \frac{1}{2}$$
  • $$\displaystyle \frac{\sqrt{3}}{2}$$
If co$$\displaystyle \sec \left ( 20^{\circ} + x \right )=\sec \left ( 50^{\circ}+x \right ) $$ the value of x is 
  • $$\displaystyle 10^{\circ}$$
  • $$\displaystyle 20^{\circ}$$
  • $$\displaystyle 30^{\circ}$$
  • $$\displaystyle 40^{\circ}$$
The value of $$\displaystyle 4\left ( \sin ^{4}30^{\circ}+\cos ^{4}30^{\circ} \right )-3\left ( \cos ^{2}45^{\circ}+\sin ^{2}90^{\circ} \right ) $$  is:
  • $$-\dfrac12$$
  • $$-2$$
  • $$2$$
  • $$\dfrac12$$
$$\displaystyle  \sin^{2} 85^{\circ} + \sin ^{2}5^{\circ} =$$ ______
  • $$0$$
  • $$1$$
  • $$\dfrac12$$
  • $$\dfrac23$$
If $$\displaystyle \sin ^{4}\theta +\cos ^{4}\theta =\dfrac{1}{2} $$ then the value of  $$\displaystyle \sin \theta \cos \theta  $$ is  
  • $$\displaystyle \pm \frac{1}{8} $$
  • $$\displaystyle \pm \frac{1}{4} $$
  • $$\displaystyle \pm 1 $$
  • $$\displaystyle \pm \frac{1}{2} $$
If $$\displaystyle  \sqrt{3}\tan \theta =3\sin \theta $$ then the value of $$\displaystyle  \sin ^{2}\theta -\cos ^{2}\theta $$ is
  • 2
  • $$\displaystyle \frac{1}{2}$$
  • $$\displaystyle \frac{1}{3}$$
  • 3
If $$\displaystyle \sin \Theta +\text{cosec }\Theta =2 $$ find the value of $$\displaystyle \cot \Theta +\cos \Theta  $$
  • $$0$$
  • $$\dfrac12$$
  • $$1$$
  • $$2$$
If $$\displaystyle X=\tan 1^{0}+\tan 2^{0}+........+\tan 45^{0}$$ and $$\displaystyle y= -(\cot 46^{0}+\cot 47^{0}+.......+\cot 89^{0})$$ then find the value of $$(x + y)$$.
  • $$1$$
  • $$0$$
  • $$-1$$
  • $$\displaystyle \dfrac {\sqrt{3}}{2}$$
$$\displaystyle \sec ^{4}\theta -\sec ^{2}\theta $$ in terms of $$\displaystyle \tan \theta  $$ is ___ 
  • $$\displaystyle \tan ^{4}\theta -\tan ^{2}\theta $$
  • $$\displaystyle \tan ^{4}\theta +\tan ^{2}\theta $$
  • $$\displaystyle \tan ^{2}\theta -\tan ^{4}\theta $$
  • None of these
If $$\displaystyle \sin \left ( A+B \right )=\dfrac{\sqrt{3}}{2}$$ and $$\displaystyle \cot  \left ( A-B \right )=\sqrt{3}$$ then find the value of $$B$$.
  • $$\displaystyle 15^{\circ}$$
  • $$\displaystyle 30^{\circ}$$
  • $$\displaystyle 10^{\circ}$$
  • $$\displaystyle 20^{\circ}$$
If $$\displaystyle \cos \Theta _{1}+\cos \Theta _{2}+\cos \Theta _{3}=3,$$ find $$\displaystyle \sin \Theta _{1}+\sin \Theta _{2}+\sin \Theta _{3}.$$
  • $$0$$
  • $$1$$
  • $$2$$
  • $$3$$
The simplified value of
$$\displaystyle \text{cosec} ^{2}\alpha \left ( 1+\frac{1}{\sec \alpha } \right )\left (1-\frac{1}{\sec \alpha }  \right )$$ is _____
  • $$1$$
  • $$0$$
  • $$2$$
  • $$-1$$
Value of $$\left(\tan{30^0}\csc{60^0} + \tan{60^0}\sec{30^0}\right)$$ is 
  • $$2\dfrac{1}{3}$$
  • $$2\dfrac{2}{3}$$
  • $$3\dfrac{1}{3}$$
  • $$\dfrac{7}{4}$$
The value of  $$\displaystyle \sin ^{2}5^{\circ}+ \sin ^{2}10^{\circ}+\sin ^{2}15^{\circ}......+\sin ^{2}90^{\circ}$$ is equal to
  • $$\dfrac{17}2$$
  • $$\dfrac{19}2$$
  • $$\dfrac{21}2$$
  • $$\dfrac{23}2$$
If $$\displaystyle\tan \theta +\cot \theta =2 $$ find the value of $$\displaystyle \tan ^{1025}\theta +\cot ^{1025}\theta $$
  • $$0$$
  • $$1$$
  • $$2$$
  • $$\dfrac12$$
If $$\displaystyle \tan \theta -\cot \theta =7  $$ find the value of $$\displaystyle \tan ^{3}\theta -\cot^{3} \theta $$
  • $$284$$
  • $$296$$
  • $$345$$
  • $$364$$
If $$\displaystyle 3\cos ^{2}A=\cos 60^{\circ}+\sin ^{2}45^{\circ} $$ then find the value of $$\displaystyle \sec ^{2}A$$.
  • $$1$$
  • $$0$$
  • $$2$$
  • $$3$$
The simplified value of $$\displaystyle \left ( \frac{1-\sin \alpha }{\cos \alpha }+\frac{\cos \alpha }{1+\sin \alpha } \right )\left ( \sec \alpha +\frac{1}{\cot \alpha } \right )$$ is _____
  • $$0$$
  • $$1$$
  • $$2$$
  • $$3$$
If $$\displaystyle \text{cosec}\, \theta -\cot \theta =2,$$ then find the value of $$\displaystyle \text{cosec} ^{2}\theta +\cot^{2} \theta.$$
  • $$\displaystyle \frac{8}{15}$$
  • $$\displaystyle \frac{15}{8}$$
  • $$\displaystyle \frac{8}{17}$$
  • $$\displaystyle \frac{17}{8}$$
In a right angled $$\triangle ABD$$, $$\angle B = 60^o$$ and $$\angle A = 30^o$$.
Then, $$\cos{60^o} = $$

453618_dbad8db06b4449d498dfa854213316b9.PNG
  • $$2$$
  • $$\dfrac{1}{2}$$
  • $$\sqrt{3}$$
  • $$\dfrac{1}{\sqrt{3}}$$
In a right angled $$\triangle ABD$$, in which $$\angle B=60^o$$ and $$\angle A=30^o$$.
Then $$\tan { 30^o }$$ is equal to

453664_e38aec4bdc7b4015aa167bb01989a95d.png
  • $$\dfrac { \sqrt { 3 } }{ 2 } $$
  • $$\dfrac { 1 }{ \sqrt { 3 } } $$
  • $$\dfrac { 2 }{ \sqrt { 3 } } $$
  • $$\sqrt { 3 } $$
In a right angled $$\triangle ABD$$, $$\angle B = 60^o$$ and $$\angle A = 30^o$$, then $$\sin{60^o} =$$
453612_a1edcf1fef6d407c9658b897f5bb79d8.png
  • $$\sqrt{3}$$
  • $$\dfrac{1}{\sqrt{3}}$$
  • $$\dfrac{\sqrt{3}}{2}$$
  • $$\dfrac{2}{\sqrt{3}}$$
In a right angled triangle, $$\angle A = \theta$$ is an acute angle.
Then, $$\cos{\theta} \times \sec{\theta}$$ is equal to
  • $$0$$
  • $$1$$
  • $$-1$$
  • None of these
In a right angle $$\triangle ABD$$, in which $$\angle B = 60^o$$ and $$\angle A = 30^o$$.
Then, $$\tan{60^o}$$ is equal to

453628_67dd6b65c9e5484fae4d0f46c6a0c442.PNG
  • $$2$$
  • $$\dfrac{1}{2}$$
  • $$\sqrt{3}$$
  • $$\dfrac{1}{\sqrt{3}}$$
In a right angle $$\triangle ABD,  \angle B=60^o$$ and $$\angle A=30^o$$.
Then $$\csc{60^o}$$ is equal to:

453641.png
  • $$\sqrt { 3 } $$
  • $$\dfrac { 2 }{ \sqrt { 3 } } $$
  • $$2$$
  • $$\dfrac { 1 }{ \sqrt { 3 } } $$
If in a rectangular, the angle between a diagonal and a side is 30$$^o$$ and the length of the diagonal is $$8$$ cm, then the area of the rectangle is _____ .
  • $$16$$$$\sqrt3$$ cm$$^2$$
  • $$16$$ cm$$^2$$
  • $$\sqrt3$$ cm$$^2$$
  • 16/$$\sqrt3$$ cm$$^2$$
0:0:1


Answered Not Answered Not Visited Correct : 0 Incorrect : 0

Practice Class 10 Maths Quiz Questions and Answers