CBSE Questions for Class 10 Maths Introduction To Trigonometry Quiz 11 - MCQExams.com

If $$\sin \theta = \dfrac {3}{5}$$, then the value of $$\text{cosec}\, \theta$$ is
  • $$\dfrac {4}{5}$$
  • $$\dfrac {5}{3}$$
  • $$\dfrac {4}{3}$$
  • $$\dfrac {5}{4}$$
The value of tan $$1^o$$ tan $$2^o$$ tan $$3^o$$.... tan $$89^o$$ is.
  • $$0$$
  • $$1$$
  • $$2$$
  • $$3$$
If $$sin^2 45 - sin^2 60 = x  cos^2 45$$ then x = ..............
  • 3/2
  • 3/4
  • -1/2
  • 2
If $$sin^2 (3x + 45) + cos^2 (2x + 60) = 1$$ then $$x =$$ ...............
  • $$60$$
  • $$30$$
  • $$15$$
  • $$0$$
Which of the following pair is a correct trignometric inter-relationship?
(1) $$\cos { \theta  } $$(a) $$\cfrac { 1 }{ \tan { \theta  }  } $$
(2) $$\tan { \theta  } $$(b) $$\cfrac { 1 }{ co\sec { \theta  }  } $$
(3) $$\cot { \theta  } $$(c) $$\cfrac { 1 }{ \sec { \theta  }  } $$
(4) $$\sin { \theta  } $$(d) $$\cfrac { 1 }{ \cot { \theta  }  } $$
  • $$1-d,2-e,3-b,4-a$$
  • $$1-b,2-a,3-e,4-d$$
  • $$1-c,2-d,3-a,4-b$$
  • $$1-e,2-b,3-c,4-d$$
The value of $$\sin 60^{\circ} \cos 30^{\circ} + \cos 60^{\circ} \sin 30^{\circ}$$ is equal to
  • $$\sec 90^{\circ}$$
  • $$\tan 90^{\circ}$$
  • $$\cos 60^{\circ}$$
  • $$\sin 90^{\circ}$$
If $$\sin { 7\theta  } =\cos { 2\theta  } $$ for acute angles $$7\theta$$ and $$2\theta$$, then $$\theta =$$
  • $$10$$
  • $$90$$
  • $$20$$
  • $$30$$
The value of $$\tan 26^{\circ}\tan 64^{\circ}$$ is
  • $$\dfrac {1}{2}$$
  • $$\dfrac {\sqrt {3}}{2}$$
  • $$0$$
  • $$1$$
If $$7\cos ^{ 2 }{ \theta  } +3\sin ^{ 2 }{ \theta  } =4$$, then $$\cot { \theta  } =$$
  • $$\cfrac { 7 }{ 3 } $$
  • $$7$$
  • $$\sqrt { 3 } $$
  • $$\cfrac { 1 }{ \sqrt { 3 } } $$
If $$ cos\, 25^0 +sin \, 25^0=k$$, then $$cos\, 20^0$$ is equal to 
  • $$\dfrac{k}{\sqrt{2}}$$
  • $$-\dfrac{k}{\sqrt{2}}$$
  • $$\pm \dfrac{k}{\sqrt{2}}$$
  • none of these
The value of $$\sec^2 \theta + \text{cosec}^2 \theta $$ is equal to :
  • $$ \tan^2 \theta + \cot^2 \theta $$
  • $$ \sec^2 \theta. \text{cosec}^2 \theta $$
  • $$ \sec \theta .\text{cosec} \theta $$
  • $$ \sin^2 \theta. \cos^2 \theta $$
  • 1
If $$\tan \theta + \cot \theta = 2$$, then the value of $$\tan^{2}\theta + \cot^{2}\theta$$ is  ____________.
  • $$4$$
  • $$2$$
  • $$\dfrac {3}{2}$$
  • $$5$$
Evaluate: $$\displaystyle\frac{-\tan\theta \cot(90^o-\theta)+\sec\theta cosec(90^o-\theta)+\sin^235^o+\sin^255^o}{\tan 10^o\tan 20^o\tan 30^o \tan 70^o \tan 80^o}$$.
  • $$\sqrt{3}$$
  • $$2\sqrt{3}$$
  • $$\displaystyle\frac{\sqrt{3}}{2}$$
  • $$1$$
If $$4\tan \theta = 3$$, then $$\dfrac {5\sin \theta + 3\cos \theta}{5\sin \theta - 3\cos \theta} = $$
  • $$9$$
  • $$5$$
  • $$10$$
  • $$4$$
The value of $$\dfrac { \sin { A }  }{ 1+\cos { A }  } +\dfrac { \sin { A }  }{ 1-\cos { A }  }$$ is $$({0}^{o}<A<{90}^{o})$$:
  • $$2\csc A$$
  • $$2\sec A$$
  • $$2\sin A$$
  • $$2\cos A$$
If $$\tan x = x - \dfrac{1}{4x}$$, then $$\sec x - \tan x$$ is equal to:
  • $$2x$$
  • $$-2x$$
  • $$4x$$
  • $$-4x$$
If : $$\tan A=\dfrac {\sqrt {3}-1}{\sqrt {3}+1}$$, then : $$\cos A=$$
  • $$\dfrac {\sqrt {3}-1}{2\sqrt {2}}$$
  • $$\dfrac {\sqrt {3}+1}{2\sqrt {2}}$$
  • $${\sqrt {3}+1}$$
  • $${\sqrt {3}-1}$$
$$(\sin A+\cos A)(1-\sin A \cos A)=\sin^3A+\cos^3 A$$
  • True
  • False
What is the value of $$\dfrac{\sin A}{1- \cos A}-\cot A = \csc A $$
  • $$1$$
  • $$2$$
  • $$5$$
  • None
State true or false.
 $$\dfrac{\cos\theta}{1-\sin\theta}= \dfrac{\tan\theta+ \sec\theta-1}{\tan\theta+ \sec\theta-1}$$
  • True
  • False
If $$\cos {\theta _1} = 2\cos {\theta _2},$$ then $$\tan \dfrac{{{\theta _1} - {\theta _2}}}{2}$$. $$\tan \dfrac{{{\theta _1} + {\theta _2}}}{2}$$ is equal to
  • $$\dfrac{1}{3}$$
  • $$\dfrac{-1}{3}$$
  • $$1$$
  • $$-1$$

In a right angled triangle, the square of the hypotenuse is twice the product of the other two sides. Then the angle of the triangle is:
  • $$15^\circ $$
  • $$30^\circ $$
  • $$45^\circ $$
  • $$60^\circ $$
$$\cos ^{ 2 }{ \theta  } \left( 1+\tan ^{ 2 }{ \theta  }  \right) +\sin ^{ 2 }{ \theta  } \left( 1+\cot ^{ 2 }{ \theta  }  \right) =2$$
  • True
  • False
If $$\sin\theta=\alpha$$ then, $$\tan\theta$$=......... .
  • $$\alpha$$
  • $$\sqrt{1-\alpha^{2}}$$
  • $$\dfrac{\alpha}{1-\alpha^{2}}$$
  • $$\dfrac{\alpha}{\sqrt{1-\alpha^{2}}}$$
Solve $$\sin A(1+\tan A)+\cos A(1+\cot A)$$.
  • $$\sec A+cosec A$$
  • $$\sin A+cos A$$
  • $$\tan A+\cot A$$
  • $$\cos A+\sin A$$
If $$\tan A+\cot A=4,\ then\ {\tan}^{4}\ A+{\cot}^{4}\ A$$ is equal to 
  • $$110$$
  • $$191$$
  • $$80$$
  • $$194$$
Check whether $$\dfrac {\cos 30^{o}+\sin 60^{o}}{1+\cos 60^{o}+\sin 30^{o}}=\dfrac {\sqrt {3}}{4}$$ is true/false ?
  • True
  • False
$$\sin^{4}\theta+2\sin^{2}\theta\left(1-\dfrac {1}{cosec^{2}\theta}\right)+ \cos^{4}\theta=$$
  • $$1$$
  • $$0$$
  • $$1/2$$
  • $$-1$$
$$sin60 ^0=\cfrac{tan30^0}{1+tan^{2}30^0}$$.
  • True
  • False
$$2 \tan 45^{\circ} + \cos 45^{\circ} - \sin 45 ^{\circ} =? $$
  • $$ 0 $$
  • $$ 1 $$
  • $$ 2 $$
  • $$ 3 $$
0:0:1


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