If sin –1 x + sin –1 y + sin –1 z = and f(1) = 2, f(p +q) …

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 = and f(1) = 2, f(p +q) = f(p). f(q) ∀ p, q ∈ R, then

– =

Text Solution

Verified by Experts

The correct answer is:

– ≤ sin –1 x ≤

∴ sin –1 x + sin –1 y + sin – 1 z =

⇔ sin –1 x = sin –1 y = sin – 1 z =

⇔ x = y = z = 1

Also f(p + q) = f(p). f(q) ∀ p, q ∈ R …(1)

Given f(1) = 1

from (1),

F(1 + 1) = f(1). F(1) ⇒ f(2) =1 2 = 1

from (2), f(2 + 1) = f(2) . f(1)

⇒ f(3) = 1 2 . 1 = 1 3 = 1

Now given expression = 3 – = 2

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