Question

If $x$ and $y$ are connected parametrically by the equation,without eliminating the parameter,find $\frac{dy}{dx}$.
$x=sin\,t,y=cos\,2t$

Answer 1

The correct answer is $-4sin\,t$
The given equations are $x=sin\,t,y=cos\,2t$
Then,$\frac{dx}{dt}=\frac{d}{dt}(sin\,t)=cos\,t$
$\frac{dy}{dt}=\frac{d}{dt}(cos\,2t)=-sin\,2t.\frac{d}{dt}(2t)=-2sin\,2t$
$∴\frac{dy}{dx}=\frac{(\frac{dy}{dt})}{(\frac{dx}{dt})}=\frac{2sin\,2t}{cos\,t}=\frac{-2.2sin\,tcos\,t}{cos\,t}=-4sin\,t$