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Q.
The solution set of the equation $\tan^{-1} x - \cot^{-1} x = \cos^{-1} (2 -x)$ will lie in the interval
Inverse Trigonometric Functions
Solution:
$\tan^{-1} x \,and \cot^{-1} x$ exist for all $ x \in R$
$ \cos^{-1} \left(2-x\right)$ exists if $ -1 \le 2 -x \le 1 $
i.e. $1 \le x \le 3 1 \le x \le 3 $