সমাধান

\(x = a(\theta + \sin\theta)\)

\(y = a(1 + \cos\theta)\)

\(\frac{dx}{d\theta} = \frac{d}{d\theta} [a(\theta + \sin\theta)] = a(1 + \cos\theta)\)

\(\frac{dy}{d\theta} = \frac{d}{d\theta} [a(1 + \cos\theta)] = a(0 - \sin\theta) = -a\sin\theta\)

\(\frac{dy}{dx} = \frac{dy/d\theta}{dx/d\theta} = \frac{-a\sin\theta}{a(1 + \cos\theta)} = \frac{-\sin\theta}{1 + \cos\theta}\)

\(\frac{dy}{dx} = \frac{-2\sin(\frac{\theta}{2})\cos(\frac{\theta}{2})}{2\cos^2(\frac{\theta}{2})} = -\frac{\sin(\frac{\theta}{2})}{\cos(\frac{\theta}{2})} = -\tan(\frac{\theta}{2})\)