Explanation

(a)
Given, $x = 2cos\theta - \cos{2\theta}$
and $y = 2\sin{\theta - \sin{2\theta}}$
$\ \frac{dx}{d\theta} = \ - 2\sin{\theta + 2\sin{2\theta}}$
and $\frac{dy}{d\theta} = 2\cos{\theta - 2\cos{2\theta}}$
$\therefore\ \ \ \ \ \frac{dy}{dx} = \frac{2\cos{\theta - 2\cos{2\theta}}}{- 2\sin{\theta + 2\sin{2\theta}}}\ \ \ \ \ \$
$= \frac{cos\theta - \cos{2\theta}}{\sin{2\theta - \sin\theta}}$
$= \frac{2\sin{\left( \frac{\theta + 2\theta}{2} \right)\sin\left( \frac{2\theta - \theta}{2} \right)}}{2\cos\left( \frac{\theta + 2\theta}{2} \right)\sin\left( \frac{2\theta - \theta}{2} \right)} = \tan\frac{3\theta}{2}$