If $y=y(x)$ is the solution of the differential equation $\left(\frac{2+\sin x}{y+1}\right) \frac{d y}{d x}+\cos x=0$ with $y(0)=1$,then $y\left(\frac{\pi}{2}\right)$ is equal to

  • A
    $\frac{1}{3}$
  • B
    $\frac{2}{3}$
  • C
    $1$
  • D
    $\frac{4}{3}$

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