If sin –1 x + sin –1 y + sin –1 z = π , then x 4 + y 4 + z …

Maths Inverse Trigonometric Functions Inverse Trigonometric Functions, Inverse Trigo Identities Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 14, 2026

If sin –1 x + sin –1 y + sin –1 z = π , then x 4 + y 4 + z 4 +

4x 2 y 2 z 2 = k (x 2 y 2 + y 2 z 2 + z 2 x 2 ), where k is equal to -

None of these

Text Solution

Verified by Experts

The correct answer is:

We have sin –1 x + sin –1 y = π – sin –1 z

or, x + y = z

or, x 2 (1– y 2 ) = z 2 + y 2 (1 – x 2 ) – 2yz

or, (x 2 – z 2 – y 2 ) 2 = 4y 2 z 2 (1 – x 2 )

or, x 4 + y 4 + z 4 – 2x 2 z 2 + 2y 2 z 2 – 2x 2 y 2 + 4x 2 y 2 z 2 – 4y 2 z 2 =0

or, x 4 + y 4 + z 4 + 4x 2 y 2 z 2 = 2(x 2 y 2 + y 2 z 2 + z 2 x 2 )

∴ k = 2.

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