Find the equations of the tangent and the normal to the curve `x=3costheta-cos^3theta,\ \ y=3sintheta-s in^3theta`

Explanation

`x=3 cos theta-cos ^{3} theta, y=3 sin theta-sin ^{3} theta `

`Rightarrow frac{d x}{d theta}=-3 sin theta+3 cos ^{2} theta sin theta`

And



`Rightarrow frac{d y}{d theta}=3 cos theta-3 sin ^{2} theta cos theta `

`Rightarrow frac{d y}{d x}=frac{frac{d y}{d theta}}{frac{d x}{d theta}}=frac{3 cos theta-3 sin ^{2} theta cos theta}{-3 sin theta+3 cos ^{2} theta sin theta}=frac{cos theta(1-sin ^{2} theta)}{-sin theta(1-cos ^{2} theta)}=frac{cos ^{3} theta}{-sin ^{3}} theta=-tan ^{3} theta`

So equation of the tangent at `theta` is

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