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Maths Trigonometrical Ratios, Functions and Identities General Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 12, 2026

The solution of inequality ≥ 6 sin x – 1 is

[ π (12n – 7)/6, π (12n + 7)/6] (n ∈ Z)

[ π (12n – 7)/6, π (12n + 1)/6] (n ∈ Z)

[ π (2n – 7)/6, π (2n + 1)/6] (n ∈ Z)

[ π (12n – 7)/3, π (12n + 1)/3] (n ∈ Z)

Text Solution

Verified by Experts

The correct answer is:

Clearly 5 – 2 sin x > 0

case-I : : If 6 sin x – 1 ≤ 0 ⇒ –1 ≤ sin x ≤

then inequality is true

case-II : : If < sin x < 1 then we have

5 – 2 sin x ≥ 36 sin 2 x – 12 sin x + 1

36 sin 2 x – 10 sin x – 4 ≤ 0 ⇒ 18 sin 2 x – 5 sin x – 2 ≤ 0

18 sin 2 x – 9 sin x + 4 sin x – 2 ≤ 0 ⇒ 9 sin x (2 sin x – 1) + 2 (2 sin x – 1) ≤ 0

⇒ (2 sin x – 1) (9 sin x + 2) ≤ 0

⇒ sin x ∈ ∴ sin x ∈

∴ sin x ∈

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