Question

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

• A. $-\sec^2(\frac{\pi}{4}-x)+c$
• B. $-\log\sec(\frac{\pi}{4}-x)+c$
• C. $\sec^2(\frac{\pi}{4}-x)+c$
• D. $\log\sec(\frac{\pi}{4}-x)+c$

Hint:

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.

Answer 1

The Correct Option is D