Trigonometry - 1

1. In △ABC, right-angled at B, AB = 5 cm and ∠ACB = 30°. Determine the lengths of the sides BC and AC.

A. 8 cm
B. 9 cm
C. 10 cm
D. 12 cm

2. In △PQR, right-angled at Q, PQ = 3 cm and PR = 6 cm. Determine ∠QPR and ∠PRQ respectively.

A. 60°, 30°
B. 30°, 60°
C. 30°, 30°
D. None of these 

3. If tan A = 4/3, then sin A = ?

A. 4/5
B. 3/5
C. 3/4
D. 1/5

4. If tan A = 3/4 & A + B = 90°, then value of cot B = ?

A. 1/5
B. 3/4
C. 4/5
D. 3/5

5. Find the value of cos37°/sin53° ?

A. 1
B. 2
C. -1
D. 0

6. If tanⲫ = a/b, then 

(a sinⲫ + b cosⲫ)/(a sinⲫ − b cosⲫ) is

A. a/(a² + b²)
B. b/(a² + b²)
C. (a² − b²)/(a² + b²)
D. (a² + b²)/(a² − b²)

7. Sin (45 + ⲫ) − cos (45 − ⲫ) is 

A. 2 sinⲫ
B. 1
C. 2 cos ⲫ
D. 0

8. If sin 17° = x/y, then value of (sec 17° − sin 73°) is

A. y²/{x√(y² − x²)}
B. x²/{y√(y² − x²)}
C. x²/{y√(x² − y²)}
D. y²/{x√(x² − y²)}

9. Find the exact value of cos 120° ?

A. 1
B. 0
C. −0.5
D. 0.5

10. What is the value of 
[(tan 5θ + tan 3θ)/{4cos 4θ (tan 5θ − tan 3θ)} ?

A. sin2θ
B. cos2θ
C. tan2θ
D. cot2θ

11. If (2sinθ − cosθ)/(cosθ + sinθ) = 1, then value of cotθ is :

A. 1/2
B. 1/3
C. 3
D. 2

12. If cos θ. cosec 23° = 1, then value of θ is 

A. 23°
B. 37°
C. 63°
D. 67°

13. If sin θ = (p² − 1) /  (p² + 1), then cos θ is

A. 2p/(1 + p²)
B. p/(p² − 1)
C. p/(1 + p²)
D. 2p/(p² − 1)

14. If (tanθ + cotθ)/(tanθ − cotθ) = 2 (0 ≤ θ ≤ 90°), then the value of sin θ is

A. 2/√3
B. √3/2
C.1/2
D. 1

15. sin²5° + sin²10° + sin²15° + ...... + sin²85° + sin²90° = ?

A. 15/2
B. 17/2
C. 9
D. 19/2

16. In a rectangle ABCD, AB = 15cm, ∠BAC = 60°, then the length of side BC is ____

A. 15√2 cm
B. 15 cm
C. 15√5 cm
D. 15√3 cm

17. If 3sinθ = 2cosθ, then

(4sinθ − cosθ)/(4cosθ + sinθ) = ?

A. 5/7
B. 5/8
C. 5/14
D. 5/11

18. If cosθ + secθ = 2, then (cos¹¹⁷θ + sec¹¹⁷θ) = ?

A. 234

B. 2

C. 2¹¹⁷

D. 117

19. (secθ − tanθ)² (1 + sinθ)² ÷ sin²θ = ?

A. cosθ

B. cot²θ

C. secθ

D. cos²θ

20. sin²36 + tan²60 + sec²30 + sin²54 = ?

A. 5

B. 17/3

C. 14/3

D. 16/3