Question

If $x=\sin t, y=\cos 2 t$, then $\frac{d y}{d x}$ is equal to

(A) $4 \sin t$

(B) $-4 \sin t$

(C) $2 \sin t$

(D) None of these

Answer 1

On differentiating, w.r.t. $t$, we get

$\begin{aligned}\frac{d x}{d t} & =\cos t, \frac{d y}{d t}=-2 \sin 2 t \\\therefore \quad \frac{d y}{d x} & =\frac{d y / d t}{d x / d t}=\frac{-2 \sin 2 t}{\cos t} \\& =-4 \sin t\end{aligned}$

So, The correct option will be (B).