Question

$y={\tan }^{-1}\frac{\sin x}{1+\cos x}$, then find $4\frac{dy}{dx}$

Answer 1

$y={\tan }^{-1}\frac{\sin x}{1+\cos x}={\tan }^{-1}\frac{2\sin \frac{x}{2}.\cos \frac{x}{2}}{2.{\cos }^2\frac{x}{2}}={\tan }^{-1}\tan \frac{x}{2}=\frac{x}{2}\therefore \frac{dy}{dx}=\frac{1}{2}$