Find x satisfying [tan –1 x] + [cot –1 x] = 2,[·] → greates…

Maths Inverse Trigonometric Functions Mix Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 11, 2026

Find x satisfying [tan –1 x] + [cot –1 x] = 2,[·] → greatest Integer function

(cot 3, cot 2)

(cot 3, – cot 1)

(cot 3, 0)

None of these

Text Solution

Verified by Experts

The correct answer is:

[cot –1 x] = 0, 1, 2, 3, [tan –1 x] = –2, –1, 0, 1

Case (i) [cot –1 x] = [tan –1 x] = 1

x ∈ (cot 2, cot 1], & x ∈ [tan 1, ∞ )

∴ x ∈φ as cot 1 < tan 1

(ii) [cot –1 x] = 3, [tan –1 x] = – 1

x ∈ (– ∞ , cot 3], x ∈ [– tan1, 0]

∴ x ∈φ as cot 3 < – tan 1

(iii) [cot –1 x] = 2, [tan –1 x] = 0

x ∈ (cot 3, cot 2], x ∈ [0, tan 1)

x ∈φ as cot 2 < 0

So no solution

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