Question

If $x=\sin t,y=\cos 2t$ then prove that $\frac{dy}{dx}=-4\sin t$.

Answer 1

Given:
$x=\sin t;y=\cos 2t$

Diff w.r.t ${}^{\prime }{t}^{\prime }$

$\therefore \frac{dx}{dt}=\cos t;\frac{dy}{dx}=-2\sin 2t$
$\therefore \frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}=\frac{-2\sin 2t}{\cos t}=\frac{-2.2\sin t\cos t}{\cos t}[\because \sin 2t=2\sin t.\cos t]$
$\therefore \frac{dy}{dx}=-4\sin t$ (proved).