Trigonometry MCQs for Competitive Examination
Solve the following problems.
Q. 21
cotθ/((1-sinθ)(secθ+tanθ))
(A) cosecθ
(B) sinθ
(C) secθ
(D) 1
Answer: (A) cosecθ
Explanation:
Q. 22
The value of
(tan13°tan37°tan45°tan53°tan77°)/(2cosec²60°(cos²60° −3cos²60°+2))
(A) 2
(B) 1
(C) 3/2
(D) 1/2
Answer: (D) 1/2
Explanation:
Q. 23
If cos²θ − sin²θ − 3cosθ+ 2 = 0, 0° < θ < 90°, then what is the value of (4cosecθ + cotθ)?
(A) 3√3
(B) 4
(C) 4√3
(D) 3
Answer: (A) 3√3
Explanation:
Q. 24
((secθ+tanθ)(1-sinθ))/(cosecθ(1+cosθ)(cosecθ-cotθ)) is equal to
(A) sinθ
(B) cosθ
(C) secθ
(D) cosecθ
Answer: (B) cosθ
Explanation:
Q. 25
If cotθ=1/√3, 0° < θ < 90° then the value of ((2-sin²θ)/(1-cos²θ))+(cosec²θ+secθ) is
(A) 4
(B) 6
(C) 7
(D) 5
Answer: (D) 5
Explanation:
Q. 26
If (1/(secθ-tanθ))-(1/cosθ)=secθ*K, 0°<θ<90°, then K is equal to
(A) cosecθ
(B) tanθ
(C) sinθ
(D) cotθ
Answer: (C) sinθ
Explanation:
Q. 27
If cosec 31°=x, then sin²59°+1/cosec²31°+tan²59°-(1/sin²59°cosec²59°) is equal to
(A) x+1
(B) x²-1
(C) x-1
(D) x²+1
Answer: (B) x²-1
Explanation:
Q. 28
((sin²25°+sin²65°)/(cos²24°+cos²66°))+sin²71°+cos71°sin19°
(A) 0
(B) 1
(C) 2
(D) 3
Answer: (C) 2
Explanation:
Q. 29
If 3sinθ=2cos²θ, 0°<θ<90°, then the value of (tanθ+cosθ+sinθ) is
(A) 5√3/3
(B) 5√3/6
(C) (3+5√3)/6
(D) (3+5√3)/3
Answer: (C) (3+5√3)/6
Explanation:
Q. 30
If 3cos²θ+6sin²θ=3, 0°<θ<90°, then the value of θ is
(A) 0°
(B) 45°
(C) 30°
(D) 90°
Answer: (A) 0°
Explanation:
Q. 31
The value of (cos 9° sin81°)(sec 9° cosec 81° )/( sin56° sec 34° + cos25° cosec65°) is
(A) 1
(B) 1/2
(C) 4
(D) 2
Answer: (B) 1/2
Explanation:
Q. 32
If sinθsec²θ=2/3, 0°<θ<90°, then the value of (tan²θ+cos²θ) is
(A) 7/6
(B) 11/12
(C) 13/12
(D) 5/4
Answer: (C) 13/12
Explanation;
Q. 33
If 3-2sin²A-3cosA=0, 0°<A<90°, then what is the value of (2cosecA+tanA)
(A) 7√3
(B) 5√3
(C) 5√3/3
(D) 7√3/3
Answer: (A) 7/√3
Explanation:
Q. 34
If 1/(1-sinθ)+1/(1+sinθ)=4secθ, 0°<A<90°, then the value of (3cotθ+cosecθ) is equal to
(A) 5√3/3
(B) 4√3
(C) 5√3
(D) 2√3/3
Answer: (C) 5/√3
Explanation:
Q. 35
If cosθ=2p/(p²+1), then sinθ is equal to
(A) (p²-1)/(p²+1)
(B) 2p/(p²-1)
(C) (p²+1)/(p²-1)
(D) 2p/(p²+1)
Answer: (A) (p²-1)/(p²+1)
Explanation:
Q. 36
If tan x = cot (65° + 9x), then what is the value of x?
(A) 2.5°
(B) 2°
(C) 1°
(D) 1.5°
Answer: (A) 2.5°
Explanation:
Q. 37
If cosX=-1/2 and π<X<3π/2, then the value of 4tan²X+3cosec²X is
(A) 16
(B) 8
(C) 4
(D) 10
Answer: (A) 16
Explanation:
Q. 38
If secθ=4X, and tanθ=4/X, (X≠0), then the value of 8(X²-1/X²) is
(A) 1/16
(B) 1/4
(C) 1/2
(D) 1/8
Answer: (C) 1/2
Explanation:
Q. 39
If θ is an acute angle, and it is given that 5 sinθ + 12 cosθ= 13, then what is the value of tanθ?
(A) 5/13
(B) 12/13
(C) 5/12
(D) 13/12
Answer: (C) 5/12
Explanation:
Q. 40
For θ being an acute angle, it is given that, 3(cosec²θ + cot² θ) = 5. Then θ is equal to
(A) 0°
(B) 30°
(C) 45°
(D) 60°
Answer: (D) 60°
Explanation: