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

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.