Solve the equation 2cos –1 x = sin –1 (2x )

Maths Inverse Trigonometric Functions Inverse Trigonometric Functions, Inverse Trigo Identities Subjective Type

Published on: August 12, 2026

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The correct answer is:

CHECK THE SOLUTION.

cos –1 x = θ ⇒ x = cos θ , 0 ≤ θ ≤ π

L.H.S. = 2 cos –1 x = 2 θ and 0 ≤ 2 θ ≤ 2 π …(1)

R.H.S. = sin –1 (2x )

= sin –1 (2 cos θ sin θ )

= sin –1 (sin 2 θ ) = 2 θ

⇒ – ≤ 2 θ ≤ ⇒ – ≤ θ ≤ …(2)

From equation (1) and eqn. (2), we have, common value of θ as: 0 ≤ θ ≤

∴ solution of the given equation is 0 ≤ θ ≤

⇒ cos 0 ≥ θ ≥ cos

⇒ 1 ≥ x ≥

⇒ ≤ x ≤ 1

⇒ x ∈

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