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# Find $\large \frac{dy}{dx}$ of the function expressed in parametric form $x=3\cos \theta-2\cos^3\theta,y=3\sin \theta-2\sin^3\theta$

Toolbox:
• To find $\large\frac{dy}{dx}$ in the case of parametric functions,if $x=\phi(t)$ and $y=\psi(t)$,then $\large\frac{dy}{dx}$$=\large\frac{\Large\frac{dy}{dt}}{\Large\frac{dx}{dt}} Step 1: Given : x=3\cos\theta-2\cos^3\theta and y=3\sin\theta-2\sin^3\theta Consider x=3\cos \theta-2\cos^3\theta Differentiating w.r.t \theta we get, \large\frac{dx}{d\theta}$$=-3\sin\theta-6\cos^2\theta(-\sin\theta)$
$\quad\;\;=-3\sin\theta+6\sin^2\theta\sin\theta$
$\quad\;\;=-3\sin\theta(2\cos^2\theta-1)$
Step 2:
Consider $y=3\sin\theta-2\sin^3\theta$
Now differentiating w.r.t $\theta$ we get,