Trigonometry MCQs

Question 1

What is the value of $$\frac{{\left( {\sin 4x + \sin 4y} ight)\left[ {	an \left( {2x - 2y} ight)} ight]}}{{\sin 4x - \sin 4y}}?$$

Accepted Answer

tan(2x + 2y)

Answer

tan2(2x + 2y)

Answer

tan 2 (x - y)

Answer

cot(x - y)

Question 2

If $$6{\sin ^4}	heta + 3{\cos ^4}	heta = 2{	ext{,}}$$ then the value of $${\left[ {7{{\operatorname{cosec} }^6}	heta + 8{{\sec }^6}	heta } ight]^{\frac{1}{3}}}$$ is?

Accepted Answer

6

Answer

2

Answer

4

Answer

8

Question 3

0 < θ < 90°, tanθ + sinθ =m and tanθ - sinθ = n, where m ≠ n, then the value of m 2 - n 2 is?

Accepted Answer

4$$\sqrt {	ext{mn}} $$

Answer

2(tan 2 θ + sin 2 θ)

Answer

4mn

Answer

2(m 2 + n 2 )

Question 4

If $$\frac{{1 + \sin 	heta }}{{1 - \sin 	heta }} = \frac{{{p^2}}}{{{q^2}}},$$ then secθ is equal to:

Accepted Answer

$$\frac{1}{2}\left( {\frac{q}{p} + \frac{p}{q}} \right)$$

Answer

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

Answer

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

Answer

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

Question 5

The value of m[sinθ + 2cos 2 ∅ + 3sinθ + 4cos 2 ∅ + . . . . . . . . + 18cos 2 ∅] is a perfect square of an integer, θ = 30°, ∅ = 45° and 150 ≤ m ≤ 180. Find the value of m.

Accepted Answer

152

Answer

161

Answer

176

Answer

168

Question 6

A coconut tree swings with the wind in such a manner that the angle covered by its trunk is 18 degrees. If the topmost portion of the tree covers a distance of 44 metres, find the length of the tree.

Accepted Answer

140 metres

Answer

120 metres

Answer

210 metres

Answer

70 metres

Question 7

The value of expression cos 2 45° + cos 2 135° + cos 2 225° + cos 2 315° is:

Accepted Answer

2

Answer

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

Answer

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

Answer

1

Question 8

If cosA + cosB + cosC = 3, then what is the value of sinA + sinB + sinC?

Accepted Answer

0

Answer

1

Answer

2

Answer

-1

Question 9

If cos(A - B) = $$\frac{{\sqrt 3 }}{2}$$ and sec A = 2, 0° ≤ A ≤ 90°, 0° ≤ B ≤ 90° then what is the measure of B?

Accepted Answer

30°

Answer

60°

Answer

0°

Answer

90°