Trigonometry MCQs for Competitive Examination
Solve the following problems.
Q. 61
What is the value of sec(-2π/3)?
(A) -2
(B) 2
(C) 2/√3
(D) -2/√3
Answer: (B) 2
Explanation:
Q. 62
What is the simplest form of (1 + cosA)(cosecA – cotA)?
(A) cosA
(B) tanA
(C) cotA
(D) sinA
Answer: (D) sinA
Explanation:
Q. 63
What is the value of sin 300°?
(A) 1
(B) -√3/2
(C) 1/2
(D) √3/2
Answer: (B) –√3/2
Explanation:
Q. 64
If (1 + secA)/tanA = x, then x is
(A) cot(A/2)
(B) tan(A/2)
(C) cosec(A/2)
(D) sec(A/2)
Answer: (A) cot(A/2)
Explanation:
Q. 65
If sec2A + cosec2A = X, then the value of X is
(A) tan2A cot2A
(B) sinA cosA
(C) secA cosecA
(D) sec2A cosec2A
Answer: (D) sec2A cosec2A
Explanation:
Q. 66
The value of (sec245 – cot245) – (sin230 + sin260) is
(A) 1
(B) 2√3
(C) 0
(D) 1/√2
Answer: (C) 0
Explanation:
Q. 67
If x=aCosθCosΦ, y = aCosθSinΦ and z= aSinθ, then the value of x2 + y2 + z2 is
(A) 2a2
(B) 4a2
(C) 9a2
(D) a2
Answer: (D) a²
Explanation:
Q. 68
If sinθ + cosθ = 1, then the sinθ cosθ is equal to
(A) 0
(B) 1
(C) 1/2
(D) -1/2
Answer: (A) 0
Explanation:
Q. 69
If (sinX+cosX)/(sinX-cosX)=3, then sin4X – cos4X is
(A) 4/3
(B) 3/4
(C) 5/3
(D) 3/5
Answer: (D) 3/5
Explanation:
Q. 70
In circular measure, the value of the angle 11°15′ is
(A) (π/16) radian
(B) (π/8) radian
(C) (π/4) radian
(D) (π/12) radian
Answer: (A) (π/16) radian
Explanation:
Q. 71
tan80° tan10° + sin270° + sin220° is
(A) 0
(B) 1
(C) 2
(D) √3/2
Answer: (C) 2
Explanation:
Q. 72
If tanθ + cotθ = 5, then the value of tan2 θ+ cot2 θ is
(A) 22
(B) 25
(C) 23
(D) 27
Answer: (C) 23
Explanation;
Q. 73
If tan3θ. tan7θ = 1, then the value of tan(θ + 36°) is
(A) 1/√3
(B) 0
(C) 1
(D) √3
Answer: (C) 1
Explanation:
Q. 74
The minimum value of 2sin2θ + 3cos2θ is
(A) 1
(B) 3
(C) 2
(D) 4
Answer: (C) 2
Explanation:
Q. 75
The value of Sin2 220 + Sin2 680 + Cot2 300 is
(A) 3/4
(B) 4
(C) 5/4
(D) 3
Answer: (B) 4
Explanation:
Q. 76
If θ be acute angle and tan (4θ – 500) = cot(500 – θ), then the value of θ in degrees is
(A) 30
(B) 40
(C) 20
(D) 50
Answer: (A) 30
Explanation:
Q. 77
If 5Sinθ = 3, the numerical value of (Secθ – Tanθ) / (Secθ + Tanθ)
(A) 1/3
(B) 1/2
(C) 1/4
(D) 1/5
Answer: (C) 1/4
Explanation:
Q. 78
If secθ + tanθ = p, (p ≠ 0) then secθ is equal to
(A) (p + 1/p), p ≠ 0
(B) (1/2)(p + 1/p), p ≠ 0
(C) 2(p – 1/p), p ≠ 0
(D) (p – 1/p), p ≠ 0
Answer: (B) (1/2)(p + 1/p), p ≠ 0
Explanation:
Q. 79
√[(1 – sinA)/(1 + sinA)] is equal to?
(A) secA – tanA
(B) cosecA – cotA
(C) secA + tanA
(D) cosecA + cotA
Answer: (C) secA+tanA
Explanation:
Q. 80
If tanA = x, then x is
(A) √(cosec²A + 1)
(B) √(sec²A + 1)
(C) √(cosec²A – 1)
(D) √(sec²A – 1)
Answer: (D) √(sec²A – 1)
Explanation: