Let $y=y(x)$ be the solution of the differential equation, ${2+\sin x\over y+1}.{dy\over dx}=-\cos x,\ y>0,\ y(0)=1$. If $y(\pi)=a$ and $dy\over dx$ at $x=\pi$ is $b$, then the ordered pair $(a, b)$ is equal to :

(1) $\left(2, {3\over2}\right)$

(2) (1, –1)

(3) (2, 1)

(4) (1, 1)

(1) $\left(2, {3\over2}\right)$

(2) (1, –1)

(3) (2, 1)

(4) (1, 1)