Question:medium

If $\frac{5\pi}{4}<x<\frac{7\pi}{4}$, then $\int \sqrt{\frac{1-\sin 2x}{1+\sin 2x}} dx =$

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When simplifying expressions like $\sqrt{1 \pm \sin 2x}$, use the perfect square identities $(\cos x \pm \sin x)^2$. Always be careful with the absolute value that results from the square root and determine the correct sign based on the given interval.

Updated On: Mar 30, 2026

$-\sec^2(\frac{\pi}{4}-x)+c$
$-\log\sec(\frac{\pi}{4}-x)+c$
$\sec^2(\frac{\pi}{4}-x)+c$
$\log\sec(\frac{\pi}{4}-x)+c$

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The Correct Option is D

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