If $(2+\sin x) \large\frac{dy}{dx}$$+(y+1) \cos x=0$ and $y(0)=1$, then $y \bigg(\large\frac{\pi}{2} \bigg)$ is equal to :

Question

$\begin{array}{1 1} (1) \large\frac{-2}{3} \\ (2) \large\frac{-1}{3} \\ (3) \large\frac{4}{3} \\ (4) \large\frac{1}{3} \end{array} $