2
###
If 3 sin x + 5 cos x = 5, then what is the value of (3 cos x – 5 sin x)

If 3 sin x + 5 cos x = 5, then what is the value of (3 cos x – 5 sin x)?

- 0
- 2
- 3
- 5

3
###
If tan (A + B) = √3 and tan A = 1, then tan (A - B) is equal to

If tan (A + B) = √3 and tan A = 1, then tan (A - B) is equal to

- 0
- 1
- 1/√3
- √2

4
###
The angles of elevation of the top of a tower from two points

The angles of elevation of the top of a tower from two points situated at distance 36 m and 64 m from its base and in the same straight line with it are complementary. What is the height of the tower?

- 48 m
- 30 m
- 25 m
- 24 m

5
###
If 2 cot θ = 3, then what is the value of

If 2 cot θ = 3, then what is the value of (2 cos θ - sin θ) / (2 cos θ + sin θ)?

- 1/3
- 1/2
- 3/4
- 2/3

6
###
The value of cosec^2 67 + sec^2 57 - cot^2 33 - tan^2 23

The value of cosec^{2} 67 + sec^{2} 57 - cot^{2} 33 - tan^{2} 23 is

- 2√2
- 2
- √2
- 0

7
###
If tan A + cot A = 4, then tan^4 A + cot^4 A

If tan A + cot A = 4, then tan^{4} A + cot^{4} A is equal to

- 194
- 191
- 110
- 80

8
###
The angle of elevation of the tip of a tower from a point

The angle of elevation of the tip of a tower from a point on the ground is 45°. Moving 21 m directly towards the base of the tower, the angle of elevation changes to 60°. What is the height of the tower, to the nearest meter?

- 48 m
- 49 m
- 50 m
- 51 m

9
###
If sin x + cos x = c, then sin^6 x + cos^6 x is equal to

If sin x + cos x = c, then sin^{6} x + cos^{6} x is equal to

- (1 + 6c
^{2}- 3c^{4})/16 - (1 + 6c
^{2}- 3c^{4})/4 - (1 + 6c
^{2}+ 3c^{4})/16 - (1 + 6c
^{2}+ 3c^{4})/4

10
###
What is the angle of elevation of the sun when the shadow

What is the angle of elevation of the sun when the shadow of a pole is √3 times the length of the pole?

- 30°
- 45°
- 60°
- 75°

11
###
From an aeroplane vertically above a straight horizontal road

From an aeroplane vertically above a straight horizontal road, the angle of depression of two consecutive kilometer stones on the opposite sides of the aeroplane are found to be α and β. The height of the aeroplane above the road is

- (tan α + tan β) / (tan α tan β)
- (tan α tan β) / (tan α + tan β)
- (cot α cot β) / (cot α + cot β)
- (cot α + cot β) / (cot α cot β)

12
###
From the top of a building 90 m high, the angles of depression

From the top of a building 90 m high, the angles of depression of the top and the bottom of a tree are 30° and 45° respectively. What is the height of the tree?

- 30√3 m
- 90 - 30√3 m
- 90 + 30√3 m
- 60 + 30√3 m

13
###
If x = a cos θ + b sin θ and y = a sin θ – b cos θ

If x = a cos θ + b sin θ and y = a sin θ – b cos θ, then what is x^{2} + y^{2} equal to?

- 2ab
- a + b
- a
^{2}+ b^{2} - a
^{2}– b^{2}

14
###
An aeroplane flying at a height of 300 m above the ground passes

An aeroplane flying at a height of 300 m above the ground passes vertically above another plane at an instant when the angles of elevation of the two planes from the same point on the ground are 60° and 45° respectively. What is the height of the lower plane from the ground?

- 100√3 m
- 100/√3 m
- 50√3 m
- 150(√3 + 1) m

15
###
If 7 sin^2 x + 3 cos^2 x = 4, then what is the value of tan x

If 7 sin^{2} x + 3 cos^{2} x = 4, 0 < x < 90°, then what is the value of tan x?

- √2
- 1
- √3/2
- 1/√3

16
###
What is the value of (Quant Trigo #01)

What is equal to?

- cos
^{2}A - sin^{2}A - cos A - sin A
- 1
- 2

18
###
What is the value of which satisfies the equation cos θ + tan θ = 1

What is the value of which satisfies the equation cos θ + tan θ = 1?

- 0°
- 30°
- 45°
- 60°

19
###
If cos θ1 + cos θ2 + cos θ3 = 3, then what is sin θ1 + sin θ2 + sin θ3

If cos θ_{1} + cos θ_{2} + cos θ_{3} = 3, then what is sin θ_{1} + sin θ_{2} + sin θ_{3} equal to?

- 0
- 1
- 2
- 3

20
###
What is the minimum value of 9 tan^2 θ + 4 cot^2 θ

What is the minimum value of 9 tan^{2} θ + 4 cot^{2} θ

- 6
- 9
- 12
- 13

21
###
If D is the number of degrees and R is the number of radians in an angle θ

If D is the number of degrees and R is the number of radians in an angle θ, then which one of the following is correct?

- πD = 180R
- πD = 90R
- πR = 180D
- πR = 90D