If $\sin y=x \sin (a+y)$, then $\frac{d y}{d x}$ is:

$\frac{\sin ^2(a+y)}{\sin a}$

The correct answer is Option (4) → $\frac{\sin ^2(a+y)}{\sin a}$

$\sin y=x \sin (a+y)$

$\frac{\sin y}{\sin (a+y)}=x$

$\frac{dx}{dy}=\frac{\cos y\sin(a+y)-\cos(a+y)\sin y}{\sin^2(a+y)}$

$=\frac{\sin a}{\sin^2(a+y)}$

$\frac{dy}{dx}=\frac{\sin^2(a+y)}{\sin a}$