If `x=2costheta-cos2theta"and"y=2sintheta-sin2theta"P r o v et h a t"` `(dy)/(dx)=tan((3theta)/2)dot`

Explanation

To prove that \(\frac{dy}{dx} = \tan\left(\frac{3\theta}{2}\right)\) given the equations \(x = 2\cos\theta - \cos 2\theta\) and \(y = 2\sin\theta - \sin 2\theta\), we will follow these steps:

### Step 1: Differentiate \(y\) with respect to \(\theta\)

Given:
\[ y = 2\sin\theta - \sin 2\theta \]
...