The value of $\cot -1 \frac{\sqrt{1-\sin x}+\sqrt{1+\sin x}}{\sqrt{1-\sin x}-\sqrt{1+\sin x}}$ if $0^{\circ} < x < 90^{\circ}$ is

JEE MATHEMATICS MCQ: INVERSE TRIGONOMETRY

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Application +4 | -1

The value of

\cot -1 \frac{\sqrt{1-\sin x}+\sqrt{1+\sin x}}{\sqrt{1-\sin x}-\sqrt{1+\sin x}}

0^{\circ} < x < 90^{\circ}

View answer and explanation

Correct option: C

\pi-\frac{x}{2}

Option C (

\pi - \frac{x}{2}

) is correct because simplifying the expression inside the

\cot^{-1}

function leads to

-\cot(\frac{x}{2})

, and using the property

\cot^{-1}(-x) = \pi - \cot^{-1}(x)

gives the result.

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