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Evaluate: \[ \cot^{-1}\!\left(\frac{\sqrt{1+\sin x} + \sqrt{1-\sin x}}{\sqrt{1+\sin x} - \sqrt{1-\sin x}}\right) \]

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Expressions with \(\sqrt{1 \pm \sin x}\) often simplify using half-angle identities: \(1 \pm \sin x = (\sin\frac{x}{2} \pm \cos\frac{x}{2})^2\).

Updated On: Apr 16, 2026

\(\frac{x}{3}\)
\(\frac{x}{4}\)
\(1\)
\(\frac{x}{2}\)

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The Correct Option is D

Solution and Explanation

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Evaluate: \[ \cot^{-1}\!\left(\frac{\sqrt{1+\sin x} + \sqrt{1-\sin x}}{\sqrt{1+\sin x} - \sqrt{1-\sin x}}\right) \]

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The Correct Option is D

Solution and Explanation

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