Trigonometry MCQs for Competitive Examination
Solve the following problems.
Q. 41
If cosθ=−(√3)/2, π<θ<3π/2, then the value of 2cot²x−3sec²x is
(A) 6
(B) 4
(C) 8
(D) 2
Answer: (D) 2
Explanation:
Q. 42
If cotθ=5x and cosecθ=5/x, (x≠0), then the value of 5(x²−1/x²) is?
(A) 1/5
(B) 1/2
(C) -1/4
(D) -1/5
Answer: (D) -1/5
Explanation:
Q. 43
Which among the following increases continuously in the range 0° < θ < 90°?
(A) cosθ
(B) tanθ
(C) cotθ
(D) cosecθ
Answer: (B) tanθ
Explanation:
Q. 44
θ being an acute angle, it is given that sec²θ+ 4tan2θ= 6. What is the value of θ?
(A) 0°
(B) 30°
(C) 45°
(D) 60°
Answer: (C) 45°
Explanation:
Q. 45
(3π/5) radians is equal to
(A) 100°
(B) 120°
(C) 108°
(D) 180°
Answer: (C) 108°
Explanation:
Q. 46
Which among the following is an irrational quantity?
(A) tan30°tan60°
(B) sin 30°
(C) tan 45°
(D) cos 30°
Answer: (D) cos30°
Explanation:
Q. 47
What is the value of cosec² 30° + sin² 45° + sec² 60° +tan² 30°?
(A) 8
(B) 53/6
(C) 9
(D) 25/3
Answer: (B) 53/6
Explanation:
Q. 48
For 0° ≤ θ ≤ 90°, what is θ , when
√3cos θ + sin θ = 1?
(A) 0°
(B) 30°
(C) 90°
(D) 60°
Answer: (D) 90°
Explanation:
Q. 49
(cosA + sinA)2 + (cosA – sinA)2 is equals to
(A) 1
(B) 1/2
(C) 2
(D) 0
Answer: (C) 2
Explanation:
Q. 50
If cosC – cosD = X, then value of X is
(A) 2sin[(C+D)/2]cos[(C-D)/2]
(B) 2cos[(C+D)/2]sin[(C-D)/2]
(C) 2sin[(C+D)/2]sin[(D-C)/2]
(D) 2cos[(C+D)/2]cos[(C-D)/2]
Answer: (C) 2sin[(C+D)/2]sin[(D-C)/2]
Explanation:
Q. 51
(1 + sinA)/(1 – sinA) is equal to?
(A) (cosecA – 1)/(cosecA + 1)
(B) (cosecA + 1)/(cosecA – 1)
(C) (secA + 1)/(secA – 1)
(D) (secA – 1)/(secA + 1)
Answer: (B) (cosecA+1)/(cosecA-1)
Explanation:
Q. 52
If sin 30° + cos 45° = X, then the value of X
(A) (2√2-√3)/2
(B) 4/√3
(C) (1-√3)/√3
(D) (1+√2)/2
Answer: (D) (1+√2)/2
Explanation;
Q. 53
What is the value of cot210°?
(A) 1/√3
(B) -1/√3
(C) √3
(D) -√3
Answer: (D) -√3
Explanation:
Q. 54
If cot(A +B) = x, then value of x is
(A) (cotAcotB + 1)/(cotB – cotA)
(B) (cotAcotB + 1)/(cotB + cotA)
(C) (cotAcotB – 1)/(cotB + cotA)
(D) (cotAcotB – 1)/(cotB – cotA)
Answer: (C) (cotAcotB-1)/(cotB+cotA)
Explanation:
Q. 55
If tan²A – sin²A = x, then value of x is
(A) tan²A sin²A
(B) cot²A cosec²A
(C) tanA sinA
(D) cotA cosecA
Answer: (A) tan²A sin²A
Explanation:
Q. 56
If 2cosAsinB = x, then the value of x is?
(A) sin(A+B) + sin(A-B)
(B) cos(A+B) + cos(A-B)
(C) sin(A+B) – sin(A-B)
(D) cos(A-B) – cos(A+B)
Answer: (C) sin(A+B) – sin(A-B)
Explanation:
Q. 57
If cosec4A – cosec²A = x, then value of x is?
(A) tan4A + tan²A
(B) cot4A + cot²A
(C) cot4A – cot²A
(D) tan4A – tan²A
Answer: (B) cot4A + cot²A
Explanation:
Q. 58
What is the value of tan(-240°)?
(A) -√3
(B) 1/√3
(C) -1/√3
(D) √3
Answer: (A) – √3
Explanation:
Q. 59
1/(secA + tanA) is equal to
(A) cosecA – cotA
(B) sinA – cosA
(C) secA – tanA
(D) sinA + cosA
Answer: (C) secA – tanA
Explanation:
Q. 60
tan(A/2) is equal to
(A) cosecA + cotA
(B) secA – cotA
(C) cosecA – cotA
(D) secA + cotA
Answer: (C) cosecA-cotA
Explanation: