If y={\Sin}^{-1} ( {\sqrt{1+ \sin x}+\sqrt{1- \sin x}}/{\sqrt{1+ \sin x}-\sqrt{1- \sin x}}) and \frac{-3 \pi}{2}< x< \frac{-\pi}{2}, then \frac{d y}{d x}= [AP EAPCET 23 May 2025 S1]

Correct Answer is : | secx2|2√cosx

- {{| {\cosec} \frac{x}{2} |}}/{2 \sqrt{ \sin ^2 \frac{x}{2}-\cos ^2 \frac{x}{2}}}

\binom{{| \sec \frac{x}{2} |}}/{2 \sqrt{\cos x}}

\binom{{| \cos \frac{x}{2} |}}/{2 \sqrt{\cos x}}

\binom{\cos \frac{x}{2}}/{\sqrt{\cos x}}

Inverse Trigonometric Functions

Section: Mathematics

Question : 14 of 33

Marks: +1, -0

If y=Sin−1(‌

√1+sin‌x+√1−sin‌x

√1+sin‌x−√1−sin‌x

) and ‌

−3π

<x<‌

−π

, then ‌

[AP EAPCET 23 May 2025 S1]

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