Trigonometry Objective Questions – MCQ with Answers

Trigonometry Objective Questions (Q75 – Q91)

Q75. If sin 2ϕ + sin 2ϕ = 1/2, cos 2ϕ + cos 2ϕ = 3/2, then cos²(2 − ϕ) =

(a) 1/5

(b) 5/5

(c) 4/5

(d) 3/5

✔ सही उत्तर: (c) 4/5

Q76. The number of solutions of the equation 3sin²x − 7sinx + 2 = 0 in the interval [0, 5π] is:

(a) 3

(b) 4

(c) 6

(d) 8

✔ सही उत्तर: (c) 6

Q77. In △ABC, a = 4, b = 5, c = 6, then ∠C is equal to:

(a) ∠A

(b) ∠2A

(c) ∠3A

(d) ∠4A

✔ सही उत्तर: (c) ∠3A

Q78. If A > 0, B > 0 and A + B = π, then the maximum value of tan A tan B is:

(a) √3

(b) 2√3

(c) 1/2

(d) 1

✔ सही उत्तर: (d) 1

Q79. Number of solutions of the equation tan x + sec x = 2 cos x in the interval (0, 2π) is:

(a) 0

(b) 2

(c) 1

(d) none of these

✔ सही उत्तर: (c) 1

Q80. In △ABC, cos A / a = cos B / b = cos C / c and a = 2. Area of the triangle is:

(a) 1

(b) √3/2

(c) √3/2

(d) √3

✔ सही उत्तर: (d) √3

Q81. In a triangle a = 13, b = 14, c = 15, then sin A/2 =

(a) 1/5

(b) √3/5

(c) √2/3

(d) √5/3

✔ सही उत्तर: (b) √3/5

Q82. In a ΔPQR, ∠R = π/2. If tan P and tan Q are the roots of the equation ax² + bx + c = 0 (a ≠ 0), then:

(a) a + b = c

(b) b + c = a

(c) c + a = b

(d) b = c

✔ सही उत्तर: (c) c + a = b

Q83. (√3 + 2 cos A)/(1 − sin A) + (1 + 2 sin A − √3)/(√3 − 2 cos A) =

(a) 1

(b) √3

(c) 0

(d) −1

✔ सही उत्तर: (c) 0

Q84. If cos A = n, sin A / sin B = m, then (m² − n²)sin² B =

(a) 1 − n²

(b) 1 + n²

(c) 1 − n

(d) 1 + n

✔ सही उत्तर: (a) 1 − n²

Q85. If (sin α + cosec α)² + (cos α + sec α)² = k + tan² α + cot² α, then k =

(a) 9

(b) 6

(c) 4

(d) 1

✔ सही उत्तर: (b) 6

Q86. sin(660°) tan(1050°) sec(−420°) cos(225°) cosec(315°) cos(90°) =

(a) √3

(b) √2

(c) 1

(d) 0

✔ सही उत्तर: (d) 0

Q87. If sin(α + β) = p, sin α + sin β = q, and cos α + cos β = r, then sin(α + β) =

(a) q² + r²

(b) √(q² + r²)

(c) q² − r²

(d) √(q² + r²) / 2

✔ सही उत्तर: (d) √(q² + r²) / 2

Q88. If tan θ₁ = k cot θ₂, then cos(θ₁ − θ₂)/cos(θ₁ + θ₂) =

(a) 1 − k / 1 + k

(b) 1 + k / 1 − k

(c) k + 1 / k − 1

(d) 1 − k² / 1 + k²

✔ सही उत्तर: (d) 1 − k² / 1 + k²

Q89. If tan θ + sec θ = √3, then the principal value of θ is:

(a) π/6

(b) π/3

(c) 2π/3

(d) 4π/3

✔ सही उत्तर: (a) π/6

Q90. If tan⁻¹ 3 + tan⁻¹ x = tan⁻¹ 8, then x =

(a) 5/14

(b) 1/14

(c) 5/11

(d) 3/11

✔ सही उत्तर: (c) 5/11

Q91. If in a triangle ABC, cos A + cos B + cos C =

(a) ≥ 3/2

(b) < 3/2

(c) > 3/2

(d) ≤ 3/2

✔ सही उत्तर: (d) ≤ 3/2