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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 1< x < , then number of solutions of the equation tan –1 (x – 1) + tan –1 x + tan –1 (x + 1) = tan –1 3x, is/are

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The correct answer is:

Given equation can be written as

tan –1 (x – 1) + tan –1 (x + 1) = tan –1 3x – tan –1 x

⇒ tan –1 = tan –1

⇒

⇒ x + 3x 3 = 2x – x 3

⇒ 4x 3 – x = 0

⇒ x(4x 2 – 1) = 0

⇒ x = 0, x = ± ½

none of which satisfies 1 < x <

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