Trigonometry MCQs

Question 1

If sinθ + cosθ = √5sin(90 - θ), find the value of cotθ

Accepted Answer

$$\frac{{\sqrt 5 + 1}}{4}$$

Answer

$$\frac{{\sqrt 5 - 1}}{5}$$

Answer

$$\frac{{\sqrt 5 + 1}}{3}$$

Answer

$$\frac{{\sqrt 5 - 1}}{4}$$

Question 2

If sec 2 A + tan 2 A = 3, then what is the value of cotA?

Accepted Answer

1

Answer

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

Answer

0

Answer

$$\sqrt 3 $$

Question 3

If $${\left( {r\cos 	heta - \sqrt 3 } ight)^2}$$ + $${\left( {r\sin 	heta - 1} ight)^2}$$ = 0, then the value of $$\frac{{r	an 	heta + \sec 	heta }}{{r\sec 	heta + 	an 	heta }}$$ is equal to?

Accepted Answer

$$\frac{4}{5}$$

Answer

$$\frac{3}{5}$$

Answer

$$\frac{{\sqrt 3 }}{4}$$

Answer

$$\frac{{\sqrt 5 }}{4}$$

Question 4

If $$\frac{{\sin 	heta }}{{1 + \cos 	heta }} + \frac{{1 + \cos 	heta }}{{\sin 	heta }} = \frac{1}{{\sqrt 3 }},$$ 0° < θ < 90° then the value of (tanθ + secθ) -1 is?

Accepted Answer

2 - √3

Answer

3 - √2

Answer

2 + √3

Answer

3 + √2

Question 5

If $$\frac{{	an 	heta + \sin 	heta }}{{	an 	heta - \sin 	heta }} = \frac{{{	ext{k}} + 1}}{{{	ext{k}} - 1}},$$ then k = ?

Accepted Answer

secθ

Answer

cosecθ

Answer

cosθ

Answer

sinθ

Question 6

$$\left( {\frac{{{{	an }^3}	heta }}{{{{\sec }^2}	heta }} + \frac{{{{\cot }^3}	heta }}{{{	ext{cose}}{{	ext{c}}^2}	heta }} + 2\sin 	heta \cos 	heta } ight)$$ ÷ (1 + cosec 2 θ + tan 2 θ), 0° < θ < 90°, is equal to:

Accepted Answer

sinθcosθ

Answer

cosecθ

Answer

cosecθsecθ

Answer

secθ

Question 7

If $$\cos 	heta = \frac{{2p}}{{1 + {p^2}}},$$ then tanθ is equal to:

Accepted Answer

$$\frac{{1 - {p^2}}}{{2p}}$$

Answer

$$\frac{{{p^2}}}{{1 + {p^2}}}$$

Answer

$$\frac{{2p}}{{1 + {p^2}}}$$

Answer

$$\frac{{1 - {p^2}}}{{1 + {p^2}}}$$

Question 8

Which of the following is equal to $$\frac{1}{{	an 	heta }} + 	an 	heta ?$$

Accepted Answer

$${	ext{cosec}}\,	heta \cdot \sec 	heta $$

Answer

$$\frac{{{	ext{cosec}}\, 	heta }}{{\sec 	heta }}$$

Answer

1

Answer

tan 2 θ

Question 9

If $${	ext{cos}}	heta = \frac{{{x^2} - {y^2}}}{{{x^2} + {y^2}}}$$ then the value of$${	ext{cot}}	heta $$ is equal to $$\left[ {{	ext{if }}{0^ \circ } \leqslant 	heta \leqslant {{90}^ \circ }} ight]$$

Accepted Answer

$$\frac{{{x^2} - {y^2}}}{{2xy}}$$

Answer

$$\frac{{2xy}}{{{x^2} - {y^2}}}$$

Answer

$$\frac{{2xy}}{{{x^2} + {y^2}}}$$

Answer

$$\frac{{{x^2} + {y^2}}}{{2xy}}$$