Question

If $y=ln\sqrt{\frac{1-\sin x}{1+\sin x}}$ then $\frac{dy}{dx}$ equals-

• A. $\sec x$
• B. $-\sec x$
• C. $\csc x$
• D. $\sec x\tan x$

Answer 1

The correct option is B $-\sec x$

$y=\ln \sqrt{\frac{1-\sin x}{1+\sin x}}$

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

$=\sec x$