Mathematics

Mathematics

Problem

Find dydx\frac{dy}{dx} , if y=cot⁡−1[1+sin⁡x+1−sin⁡x1+sin⁡x−1−sin⁡x],0<x<π2.y = \cot^{-1} \left[ \frac{\sqrt{1 + \sin x} + \sqrt{1 - \sin x}}{\sqrt{1 + \sin x} - \sqrt{1 - \sin x}} \right], \quad 0 < x < \frac{\pi}{2}.

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