The number of solutions of equation π cot –1 (x–1) + ( π –1…

Maths Inverse Trigonometric Functions Mix Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

The number of solutions of equation

π cot –1 (x–1) + ( π –1) cot –1 x = 2 π – 1

Text Solution

Verified by Experts

The correct answer is:

Let f(x) = π cot –1 (x–1) + ( π – 1) cot –1 x

f ′ (x) = < 0 ∀ ∀ x ∈ R

Hence f(x) is decreasing function and 0 < f(x) < π (2 π –1)

∴ f(x) = 2 π –1 has only one solution

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