Let y=y(x) be the solution of the differential equation, (2+ sin x)/(y+1) · (d y)/(d x)=- cos x, y>0, y(0)=1. If y(π)= a and (d y)/(d x) at x=π is b,…

Let $\displaystyle y=y(x)$ be the solution of the differential equation, $$\frac{2+\sin x}{y+1} \cdot \frac{\mathrm{~d} y}{\mathrm{~d} x}=-\cos x, y>0, y(0)=1 \text {. If } $$ $\displaystyle y(\pi)=\mathrm{a}$ and $\displaystyle \frac{\mathrm{d} y}{\mathrm{~d} x}$ at $\displaystyle x=\pi$ is b , then the ordered pair $\displaystyle (\mathrm{a}, \mathrm{b})$ is equal to :