$x = \sin t,y = \cos 2t$

Here,$x = \sin t$ …(i)
and $y = \cos 2t$ …(ii)
Differentiating (i) \& (ii) w.r.t. t, we get

$\cfrac{{dx}}{{dt}} = \cos t$ and

$\cfrac{{dy}}{{dt}} = - \sin 2t \cdot 2 = - 2\sin 2t$

therefore, $\cfrac{{dy}}{{dx}} = \cfrac{{dy/dt}}{{dx/dt}} = \cfrac{{ - 2\sin 2t}}{{\cos t}} = \cfrac{{ - 2 \cdot 2\sin t\cos t}}{{\cos t}} = - 4\sin t$