Trigonometry MCQs

Question 1

The expression of $$\frac{{\cot 	heta + \operatorname{cosec} 	heta - 1}}{{\cot 	heta + \operatorname{cosec} 	heta + 1}}$$ is equal to?

Accepted Answer

$$\frac{{1 - \cos 	heta }}{{\sin 	heta }}$$

Answer

$$\frac{{1 + \cos 	heta }}{{\sin 	heta }}$$

Answer

$$\frac{{\cot 	heta + 1}}{{\operatorname{cosec} 	heta }}$$

Answer

$$\frac{{\cot 	heta - 1}}{{\sin 	heta }}$$

Question 2

Evaluate the following expression in terms of trigonometric ratios. $$\frac{{{{\cot }^2}A\left( {\sec A - 1} \right)}}{{1 + \sin A}}$$

Accepted Answer

$$\frac{{{{\sec }^2}A\left( {1 - \sin A} \right)}}{{1 + \sec A}}$$

Answer

$$\frac{{{{\sec }^2}A\left( {1 + \sin A} \right)}}{{1 - \sec A}}$$

Answer

$$\frac{{{{\cot }^2}A\left( {1 + \sin A} \right)}}{{1 - \sec A}}$$

Answer

$$\frac{{{{\cot }^2}A\left( {1 - \sin A} \right)}}{{1 - \sec A}}$$

Question 3

What is $$\sin \alpha - \sin \beta = ?$$

Accepted Answer

$$2\cos \frac{{\alpha + \beta }}{2}\sin \frac{{\alpha - \beta }}{2}$$

Answer

$$2\sin \frac{{\alpha + \beta }}{2}\sin \frac{{\alpha - \beta }}{2}$$

Answer

$$2\cos \frac{{\alpha - \beta }}{2}\sin \frac{{\alpha + \beta }}{2}$$

Answer

$$2\cos \frac{{\alpha + \beta }}{2}\cos \frac{{\alpha - \beta }}{2}$$

Question 4

If $${	ext{tan}}\left( {\frac{\pi }{2} - \frac{	heta }{2}} ight) = \sqrt 3 $$ the value of cosθ is?

Accepted Answer

$$\frac{1}{2}$$

Answer

0

Answer

$$\frac{1}{{\sqrt 2 }}$$

Answer

1

Question 5

Which of the following will satisfy a 2 = b 2 + (ab) 2 for the values a and b?

Accepted Answer

a = cotx, b = cosx

Answer

a = sinx, b = cotx

Answer

a = cosx, b = tanx

Answer

a = sinx, b = tanx

Question 6

$${\left( {\frac{{\sin 	heta - 2{{\sin }^3}	heta }}{{2{{\cos }^3} - \cos 	heta }}} ight)^2} + 1,$$ θ ≠ 45° is equal to:

Accepted Answer

sec 2 θ

Answer

cosec 2 θ

Answer

cot 2 θ

Answer

2tan 2 θ

Question 7

The measure of the angles of a triangle are in the ratio 2 : 7 : 11. Measures of angles are ?

Accepted Answer

18°, 63°, 99°

Answer

16°, 56°, 88°

Answer

20°, 70°, 90°

Answer

25°, 175°, 105°

Question 8

If cos27° = x, then the value of tan63° is?

Accepted Answer

$$\frac{x}{{\sqrt {1 - {x^2}} }}$$

Answer

$$\frac{x}{{\sqrt {1 + {x^2}} }}$$

Answer

$$\frac{{\sqrt {1 - {x^2}} }}{x}$$

Answer

$$\frac{{\sqrt {1 + {x^2}} }}{x}$$

Question 9

If √3tanθ = 3sinθ, then what is the value of sin 2 θ - cos 2 θ?

Accepted Answer

$$\frac{1}{3}$$

Answer

$$\frac{1}{2}$$

Answer

$$\frac{1}{5}$$

Answer

$$\frac{1}{4}$$