Question

Find the derivative of $y=\ln \sqrt{\frac{1-\sin x}{1+\sin x}}$

Answer 1

$y=\frac{1}{2}\ln (1-\sin x)-\frac{1}{2}\ln (1+\sin x)$

$\frac{dy}{dx}=\frac{1}{2}(\frac{-\cos x}{1-\sin x}-\frac{\cos x}{1+\sin x})=\frac{-\cos x}{{\cos }^{2}x}=-\frac{1}{\cos x}$