Integrate: $\int \limits_{0}^{\large\frac{\pi}{2}} \large\frac{\cos x}{(1+\sin x)(2+ \sin x)}$$dx$

Question

$$\begin {array} {1 1} (a)\;\log \frac{4}{3} \\ (b)\;\log \frac{1}{3} \\ (c)\;\log \bigg(\frac{1}{4}\bigg) \\ (d)\;None \end {array}$$