Trigonometry MCQs

Question 1

$$\frac{{{	ext{cos }}\alpha }}{{{	ext{sin }}\beta }} = n$$ and $$\frac{{{	ext{cos }}\alpha }}{{{	ext{cos }}\beta }} = m,$$ then the value of $${	ext{co}}{{	ext{s}}^2}\beta $$ is?

Accepted Answer

$$\frac{{{n^2}}}{{{m^2} + {n^2}}}$$

Answer

$$\frac{{{m^2} - 1}}{{{n^2} - 1}}$$

Answer

$$\frac{{{m^2} - 3}}{{{n^2} - 4}}$$

Answer

$$\frac{{{m^2} + 3}}{{{n^2} + 3}}$$

Question 2

Let 0° < θ < 90°, (1 + cot 2 θ)(1 + tan 2 θ) × (sinθ - cosecθ)(cosθ - secθ) is equal to:

Accepted Answer

secθcosecθ

Answer

sinθcosθ

Answer

secθ + cosecθ

Answer

sinθ + cosθ

Question 3

If tanθ = tan30° .tan60° and θ is an acute angle, then 2θ is equal to?

Accepted Answer

90°

Answer

30°

Answer

45°

Answer

0°

Question 4

If tanθ + cotθ = -2, then the value of tan 9 θ + cot 9 θ is:

Accepted Answer

-2

Answer

0

Answer

2

Answer

-1

Question 5

The value of following is : $$\frac{{\sin 	heta .\operatorname{cosec} 	heta .	an 	heta .\cot 	heta }}{{{{\sin }^2}	heta + {	ext{co}}{{	ext{s}}^2}	heta }}$$ ?

Accepted Answer

1

Answer

2

Answer

0

Answer

tanθ

Question 6

The value of (cosec a - sin a)(sec a - cos a)(tan a + cot a) is?

Accepted Answer

1

Answer

4

Answer

6

Answer

2

Question 7

If sin7x = cos11x, then the value of tan9x + cot9x is?

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 8

Which of the following is equal to $$\left[ {\frac{{	an 	heta + \sec 	heta - 1}}{{	an 	heta - \sec 	heta + 1}}} ight]?$$

Accepted Answer

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

Answer

$$\frac{{1 + 	an 	heta }}{{\cot 	heta }}$$

Answer

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

Answer

$$\frac{{1 + \cot 	heta }}{{	an 	heta }}$$

Question 9

If a = 45° and b = 15°, what is the value of $$\frac{{\cos \left( {a - b} \right) - \cos \left( {a + b} \right)}}{{\cos \left( {a - b} \right) + \cos \left( {a + b} \right)}}?$$

Accepted Answer

2 - √3

Answer

2 - 2√2

Answer

3 - √6

Answer

3 - √2