Quant Trigo

What is θ equal to

If with 0 < θ < 90°, then what is θ equal to?

30°
45°
60°
75°

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)?

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

0
1
1/√3
√2

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

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)?

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

The value of cosec² 67 + sec² 57 - cot² 33 - tan² 23 is

2√2
2
√2
0

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

If tan A + cot A = 4, then tan⁴ A + cot⁴ A is equal to

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

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

If sin x + cos x = c, then sin⁶ x + cos⁶ x is equal to

(1 + 6c² - 3c⁴)/16
(1 + 6c² - 3c⁴)/4
(1 + 6c² + 3c⁴)/16
(1 + 6c² + 3c⁴)/4

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°

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)

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

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 x² + y² equal to?

2ab
a + b
a² + b²
a² – b²

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?