Trigonometry MCQs

Question 1

If x = 8(sinθ + cosθ) and y = 9(sinθ - cosθ), then the value of $$\frac{{{x^2}}}{{{8^2}}} + \frac{{{y^2}}}{{{9^2}}}$$ is:

Accepted Answer

2

Answer

4

Answer

6

Answer

8

Question 2

The value of $$\frac{{{	ext{sin 6}}{5^ \circ }}}{{\cos {{25}^ \circ }}}$$ is?

Accepted Answer

1

Answer

0

Answer

2

Answer

No defined

Question 3

Simplify the following expression cosec 4 A(1 - cos 4 A) - 2cot 2 A - 1

Accepted Answer

0

Answer

sin 2 A

Answer

cosec 2 A

Answer

1

Question 4

If $$\frac{{{{\sin }^2}	heta - 3\sin 	heta + 2}}{{{{\cos }^2}	heta }} = 1,$$ where 0° < θ < 90°, then what is the value of (cos2θ + sin3θ + cosec2θ)?

Accepted Answer

$$\frac{{9 + 4\sqrt 3 }}{6}$$

Answer

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

Answer

$$\frac{{3 + 4\sqrt 3 }}{6}$$

Answer

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

Question 5

What is the value of $$\frac{{{{\left[ {1 - 	an \left( {{{90}^ \circ } - 	heta } ight)} ight]}^2}}}{{\left[ {{{\cos }^2}\left( {{{90}^ \circ } - 	heta } ight)} ight]}} - 1 = ?$$

Accepted Answer

-sin2θ

Answer

-cos2θ

Answer

cos2θ

Answer

sin2θ

Question 6

If 2cos 2 θ + 3sinθ = 3, where 0° < θ < 90°, then what is the value of sin 2 2θ + cos 2 θ + tan 2 2θ + cosec 2 2θ?

Accepted Answer

$$\frac{{35}}{6}$$

Answer

$$\frac{{29}}{6}$$

Answer

$$\frac{{29}}{3}$$

Answer

$$\frac{{35}}{{12}}$$

Question 7

In sin(A - B) = $$\frac{1}{2}$$ and cos(A + B) =$$\frac{1}{2}$$ where A > B > 0 and A + B is an acute angle, then the value of B is?

Accepted Answer

$$\frac{\pi }{{12}}$$

Answer

$$\frac{\pi }{6}$$

Answer

$$\frac{\pi }{4}$$

Answer

$$\frac{\pi }{2}$$

Question 8

θ is the positive acute angle and sinθ - cosθ = 0, then the value of secθ + cosecθ is?

Accepted Answer

$${	ext{2}}\sqrt 2 $$

Answer

2

Answer

$$\sqrt 2 $$

Answer

$${	ext{3}}\sqrt 2 $$

Question 9

(sinθ + cosecθ) 2 + (cosθ + secθ) 2 - 1 = . . . . . . . .

Accepted Answer

6 + tan 2 θ + cot 2 θ

Answer

tan 2 θ - cot 2 θ

Answer

sin 2 θ - cot 2 θ

Answer

6 - sin 2 θ + cos 2 θ