Question
If $x=f(t), y=g(t)$ are differentiable functions of parameter ' $t$ ' then prove that $y$ is a differentiable function of ' $x$ ' and $\frac{d y}{d x}=\frac{\left(\frac{d y}{d t}\right)}{\left(\frac{d x}{d t}\right)}, \frac{d x}{d t} \neq 0$. Hence find $\frac{d y}{d x}$ if $x=a \cos t, y=a \sin t$.