If $\int \large\frac{\sin x}{\cos x(1+\cos x)dx}$$=f(x)+c$ then $f(x)$ is equal to :

Question

$$\begin {array} {1 1} (a)\;\log \bigg|\frac{1+\cos x}{\cos x}\bigg| & \quad (b)\;\log \bigg|\frac{\cos x}{1+\cos x}\bigg| \\ (c)\;\log \bigg|\frac{\sin x}{1+\sin x}\bigg| & \quad (d)\;\log \bigg|\frac{1+\sin x}{\sin x}\bigg| \end {array}$$