Trigonometry - 2

1. Evaluate : 1/(1 + sinθ) + 1/(1 − sinθ)

A. sec²θ

B. 2sec²θ

C. 2secθ

D. secθ

2. Find value of (tanθ + sinθ)/(tanθ − sinθ).

A. (secθ + 1)/2

B. (secθ + 1)/(secθ − 1)

C.  (secθ − 1)/(secθ + 1)

D. 2secθ/(secθ + 1)

3. tan²θ + cot²θ + 2 = ?

A. cosec²θ

B. sec²θ

C. cosec ²θ. sec²θ

D. cosec ²θ + sec²θ

4. If cosθ + sinθ = √2 cosθ, then cosθ − sinθ = ?

A. 2sinθ

B. √2sinθ

C. sinθ

D. √3sinθ

5. If coesc θ = 13/12, then sinθ + cosθ − tanθ = ?

A. 91/65

B. 139/65

C. 71/65

D. None

6. If θ lies in the first quadrant and cos²θ − sin²θ = 1/2, then tan²2θ + sin²3θ = ?

A. 7/2

B. 3

C. 4

D. 4/3

7. If tan A = 1/2 and tan B = 2/3, then the value of A + B is:

A. 60°

B. 15°

C. 30°

D. 45°

8. In right angled triangle ABC, if  ∠A= 30°, find the value of 3 sin A - 4 sin³ A.

A. 2

B. -1

C. -2

D. 1

9. The angle of elevation of the top of a tower from the point P and Q at distance of 'a' and 'b' respectively from the base of the tower and in the same straight line with it are complementary. The height of the tower is

A.√ab 

B. a/b

C. ab

D. a²b²

10. Two points P and Q are at the distance of x and y (where y>x respectively from the base of a building and on a straight line. If the angles of elevation of the top of the building from points P and 9 are complemen- tary, then what is the height of the building?

A. xy

B. √(y/x)

C. √(x/y)

D. √(xy)

11. The value of (1 + sin⁴ A- cos⁴A) cosec² A is:

A. -2 

B. 2 

C. 1

D. -1

12. In △DEF measure of angle E is 90°. If sec D= 25/7 and DE = 1.4 cm., then what is the length (in cm.) of side DF?

A. 5

B. 4.8

C. 4

D. 5.6

13. △PQR is right angled at Q. If cos P = 5/13 then what is the value of cosec R?

A. 13/5

B. 5/12

C. 5/13

D. 13/12

14. From the top of a tower, the angle of depression of the top of a 10 metre high building is 60°. If the distance between the tower and the building is 50√3 metre, find the height of the tower. 

A. 140 m 

B. 100 m

C. 150 m

D. 160 m

15. From the top of a 195 metre high cliff, the angles of depression of the top and bottom of a tower are 30° and 60°, respectively. Find the height of the tower (in metre).

A. 195√3

B. 130

C. 195

D. 65

16. From a point 12 metre above the water level, the angle of elevation of the top of a hill is 60°and the angle of depression of the base of the hill is 30°. What is the height (in metre) of the hill?

A. 36

B. 48

C. 48√3

D. 36√3

17. The tops of two poles of height 60 metres and 35 metres are connected by a rope. If the rope makes an angle with the horizontal whose tangent is 5/9 metres, then what is the distance (in metres) between the two poles?

A. 63

B. 25

C. 30

D. 45

18. If sin 5θ = cos (50° - 3θ), then is equal to:

A. 20°

B. 25°

C. 30°

D. 15°

19. From the top of a hill 240 m high, the angles of depression of the top and bottom of a pole are 30° and 60° respectively. The difference (in m) between the height of the pole and its distance from the hill is:

A. 120 (2-√3)

B. 120 (√3-1)

C. 80 (√3-1)

D. 80 (2-√3)

20. If sinθ cosθ = √2/3, then the value of (sin⁶θ + cos⁶θ) is :

A. 1/3

B. 4/3

C. 2/3

D. 5/3