If `xsin(a+y)+sinacos(a+y)=0` , prove that `(dy)/(dx)=(s in^2(a+y))/(sina)` .

Explanation

Given, `x \sin (a+y)+\sin a \cos (a+y)=0`
$$ x=\frac{-\sin a \cos (a+y)}{\sin (a+y)} $$
On differentiating both sides w.r.t. y, we get
$$
\frac{d x}{d y}=-\frac{\left[\begin{array}{c}
\sin (a+y) \frac{d}{d y}\{\sin a \cos (a+y)\} \\
...