$\begin{aligned} \sin y= & x \sin (a+y) \Rightarrow x=\frac{\sin y}{\sin (a+y)} \\ \Rightarrow 1 & =\frac{\cos y \cdot \frac{d y}{d x} \cdot \sin (a+y)-\sin y \cos (a+y) \frac{d y}{d x}}{\sin ^2(a+y)} \\ & =\frac{\frac{d y}{d x} \cdot \sin (a+y-y)}{\sin ^2(a+y)} \Rightarrow \frac{d y}{d x}=\frac{\sin ^2(a+y)}{\sin a},\end{aligned}$