Explanation

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