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The solution set of the equation tan^–1x – cot^–1x = cos^–1(2 – x) is

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[0, 1]

[– 1, 1]

none of these

[1, 3]

answer is C.

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Detailed Solution

tan^–1x and cot^–1x exist for all x ∈ R.
cos^–1(2 – x) exists if – 1 ≤ 2 – x ≤ 1 i.e. 1 ≤ x ≤ 3
So, the given equation holds for 1 ≤ x ≤ 3.

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