Trigonometry MCQs for Competitive Examination
Solve the following problems.
Q. 81
If sec 15θ = cosec 15θ (0° < θ < 10°), then value of θ is
(A) 9°
(B) 5°
(C) 8°
(D) 3°
Answer: (D) 3°
Explanation:
Q. 82
If tan θ − tan 30° tan 60° and θ is an acute angle, then 2θ is equal to
(A) 0°
(B) 30°
(C) 45°
(D) 90°
Answer: (D) 90°
Explanation:
Q. 83
If tan(5x – 10°) = cot(5y + 20°), then the value of (x + y) is
(A) 15°
(B) 16°
(C) 24°
(D) 20°
Answer: (B) 16°
Explanation:
Q. 84
If 0° ≤ A ≤ 90°, the simplified form of the given expression sin A cos A (tan A – cot A) is
(A) 1
(B) 1 – 2 sin²A
(C) 2 sin²A – 1
(D) 1 – cos A
Answer: (C) 2 sin²A – 1
Explanation:
Q. 85
If θ is an acute angle and tan²θ +(1/tan²θ)=2, then the value of θ is
(A) 15°
(B) 30°
(C) 45°
(D) 60°
Answer: (C) 45°
Explanation:
Q. 86
If the sum and difference of two angles are 22/9 radian and 36° respectively, then the value of the smaller angle in degree taking the value of π as 22/ 7 is
(A) 52°
(B) 60°
(C) 56°
(D) 48°
Answer: (A) 52°
Explanation:
Q. 87
The value of cos 1° cos 2° cos 3° … cos 180° is
(A) 0
(B) 1
(C) 1/2
(D) (√3)/2
Answer: (A) 0
Explanation:
Q. 88
If cos 20° = m and cos 70° = n, then the value of m² + n² is
(A) 1/2
(B) 1
(C) 3/2
(D) 1/√2
Answer: (B) 1
Explanation:
Q. 89
If 1 + cos²θ = 3 sinθ cosθ, then the integral value of cotθ(0<θ<π/2) is
(A) 0
(B) 1
(C) 2
(D) 3
Answer: (B) 1
Explanation:
Q. 90
If secθ + tanθ = 2 +√5, then the value of sinθ is (0° ≤ θ ≤ 90°)
(A) (√3)/2
(B) 2/√5
(C) 1/√5
(D) 4/5
Answer: (A) (√3)/2
Explanation:
Q. 91
Which of the following relations is correct for 0< θ<90?
(A) sinθ = sin2θ
(B) sinθ < sin2θ
(C) sinθ > sin2θ
(D) sinθ = cosecθ
Answer: (B) sinθ < sin2θ
Explanation:
Q. 92
The value of
sinθ/(1+cosθ)+sinθ/(1-cosθ)
(A) 2sinθ
(B) 2cosθ
(C) 2secθ
(D) 2cosecθ
Answer: (D) 2cosecθ
Explanation;
Q. 93
If tanθ=8/15, the value of √(1-sinθ)/√(1+sinθ) is
(A) 1/5
(B) 2/5
(C) 3/5
(D) 0
Answer: (C) 3/5
Explanation:
Q. 94
If tan45 = cotθ, then the value of θ in radians in?
(A) π/4
(B) π/9
(C) π/2
(D) π/12
Answer: (A) π/4
Explanation:
Q. 95
If cos4θ – sin4θ = 1/3, then the value of tan²θ is
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/5
Answer: (A) 1/2
Explanation:
Q. 96
If cos θ + sin θ = m and sec θ + cosecθ = n, then the value of n(m² – 1) is equal to
(A) 2n
(B) mn
(C) 2m
(D) 4mn
Answer: (C) 2m
Explanation:
Q. 97
If θ is a positive acute angle and 3(sec²θ + tan²θ) = 5, then the value of cos 2θ is
(A) 1/2
(B) 1/√2
(C) 1
(D) (√3)/2
Answer: (A) 1/2
Explanation:
Q. 98
If sec θ – cos θ =3/2, where θ is a positive acute angle, then the value of sec θ is
(A) 0
(B) 1
(C) 2
(D) -1/2
Answer: (C) 2
Explanation:
Q. 99
If tan(5x – 10°) = cot(5y + 20°), then the value of (x + y) is
(A) 15°
(B) 16°
(C) 20°
(D) 24°
Answer: (D) 24°
Explanation:
Q. 100
If x = a (sin θ + cos θ) and y = b (sin θ – cos θ), then the value of
(x/a)²+(y/b)² is
(A) 1
(B) 2
(C) 3
(D) 4
Answer: (B) 2
Explanation: