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Question

Mathematics Question on Trigonometry

The value of
cot⁡−1[1−sin⁡x+1+sin⁡x1−sin⁡x−1+sin⁡x]\cot^{-1}[\frac{\sqrt{1-\sin x}+\sqrt{1+\sin x}}{\sqrt{1-\sin x}-\sqrt{1+\sin x}}] where x ∈ (0,π4)(0,\frac{\pi}{4}) is

A

π−x3\pi-\frac{x}{3}

B

x2\frac{x}{2}

C

π−x2\pi-\frac{x}{2}

D

x2−π\frac{x}{2}-\pi

Answer

π−x2\pi-\frac{x}{2}

Explanation

Solution

The correct answer is (C) : π−x2\pi-\frac{x}{2}.