If cos –1 x + cos –1 y + cos –1 z = π , then-

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

Published by: CGP EDU Academic Team

Published on: August 13, 2026

x 2 + y 2 + z 2 + xyz = 0

x 2 + y 2 + z 2 + 2xyz = 0

x 2 + y 2 + z 2 + xyz = 1

x 2 + y 2 + z 2 + 2xyz = 1

Text Solution

Verified by Experts

The correct answer is:

⇒ cos –1 (x) + cos –1 (y) + cos –1 (z) = cos –1 (–1)

⇒ cos –1 (x) + cos –1 (y) = cos –1 (–1) – cos –1 (z)

⇒ cos –1 (xy – ) = cos –1 {(–1)(z)}

⇒ xy – = –z

squaring both sides we get

x 2 + y 2 + z 2 + 2xyz = 1

Trick : Put x = y = z =

so cos –1 +cos –1 + cos –1 = π

Obviously holds for these values of x, y, z.

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