Question:
If $y-x \sin y$, prove that $\frac{d y}{d x}=\frac{\sin y}{(1-x \cos y)}$
Solution:
We are given with an equation $y=x \sin y$, we have to prove that $\frac{d y}{d x}=\frac{\sin y}{1-x \cos y}$ by using the given equation
we will first find the value of $\frac{d y}{d x}$ and we will put this in the equation we have to prove, so by differentiating the equation on both sides with respect to $x$, we get,
$\frac{d y}{d x}=\sin y+x \cos y \frac{d y}{d x}$
$\frac{d y}{d x}[1-x \cos y]=\sin y$
$\frac{d y}{d x}=\frac{\sin y}{1-x \cos y}$