Evaluate , where…

MATHEMATICS · Subjective · CBSE · Mathematics · Inverse Trigonometric Functions · Inverse Trigonometric Functions

Problem

Evaluate cot⁡−1[1+sin⁡x+1−sin⁡x1+sin⁡x−1−sin⁡x]\cot^{-1}\left[\frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}}\right], where 0<x<π20<x<\frac{\pi}{2}.

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