Question
If $x=f(t)$ and $y=g(t)$ are differentiable function of $t$, then prove that $y$ is a differentlable function of $x$ and $\frac{d y}{d x}=\frac{\frac{d y}{d t}}{\frac{d x}{d t}}$, where $\frac{d x}{d t} \neq 0$. Hence find $\frac{d y}{d x}$ if $x=a \cos ^2 t$ and $y=a \sin ^2 t$