If $y=y(x)$ is the solution of the differential equation $\bigg(\large\frac{2+ \sin x}{y+1}\bigg) \frac{dy}{dx}$$+ cos x=0$ with $y(0)=1,$ then $y\bigg(\large\frac{\pi}{2}\bigg)=$

Question

$$\begin {array} {1 1} (a)\;\frac{1}{3} & \quad (b)\;\frac{2}{3} \\ (c)\;1 & \quad (d)\;\frac{4}{3} \end {array}$$