Trigonometry MCQs

Question 1

If tanθ + secθ = $$\frac{{x - 2}}{{x + 2}},$$ then what is the value of cosθ?

Accepted Answer

$$\frac{{{x^2} - 4}}{{{x^2} + 4}}$$

Answer

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

Answer

$$\frac{{2{x^2} - 4}}{{2{x^2} + 4}}$$

Answer

$$\frac{{{x^2} - 2}}{{{x^2} + 2}}$$

Question 2

If α and β are positive acute angles, sin(4α - β) = 1 and cos(2α + β) = $$\frac{1}{2}{	ext{,}}$$ then the value of sin(α + 2β) is?

Accepted Answer

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

Answer

0

Answer

1

Answer

$$\frac{{\sqrt 3 }}{2}$$

Question 3

The simplified value of (sec x sec y + tan x tan y) 2 - (sec x tan y + tan x sec y) 2

Accepted Answer

1

Answer

-1

Answer

0

Answer

sec 2 x

Question 4

The value of $$\frac{{\sin {{25}^ \circ }.\cos {{65}^ \circ } + \cos {{25}^ \circ }.\sin {{65}^ \circ }}}{{{{	an }^2}{{70}^ \circ } - {	ext{cose}}{{	ext{c}}^2}{{20}^ \circ }}}$$ is?

Accepted Answer

-1

Answer

0

Answer

1

Answer

2

Question 5

If $${\left\{ {\left( {\frac{{\sec 	heta - 1}}{{\sec 	heta + 1}}} ight)} ight\}^n} = {	ext{cosec}}\,	heta - \cot 	heta ,$$ then n = ?

Accepted Answer

0.5

Answer

1

Answer

-1

Answer

-0.5

Question 6

If sinθ + cosθ = $$\sqrt 2 $$ sin(90° - θ) then the value of cotθ is?

Accepted Answer

$$\sqrt 2 $$ + 1

Answer

-$$\sqrt 2 $$ - 1

Answer

$$\sqrt 2 $$ - 1

Answer

-$$\sqrt 2 $$ + 1

Question 7

If sec 2 θ + tan 2 θ = $$3\frac{1}{2},$$ 0° < θ < 90°, then (cosθ + sinθ) is equal to

Accepted Answer

$$\frac{{2 + \sqrt 5 }}{3}$$

Answer

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

Answer

$$\frac{{1 + \sqrt 5 }}{6}$$

Answer

$$\frac{{9 + 2\sqrt 5 }}{6}$$

Question 8

If θ lies in the first quadrant and cos 2 θ - sin 2 θ = $$\frac{1}{2}$$, then the value of tan 2 2θ + sin 2 3θ is:

Accepted Answer

4

Answer

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

Answer

3

Answer

$$\frac{7}{2}$$

Question 9

If cosθ = $$\frac{{12}}{{13}},$$ then the value of $$\frac{{\sin 	heta \left( {1 - 	an 	heta } ight)}}{{	an 	heta \left( {1 + {	ext{cosec}}	heta } ight)}}$$ is:

Accepted Answer

$$\frac{{35}}{{234}}$$

Answer

$$\frac{{25}}{{156}}$$

Answer

$$\frac{{35}}{{108}}$$

Answer

$$\frac{{25}}{{78}}$$