If y = a(1 + cos t) and x = a(t – sin t), then $\frac{dy}{dx}$ is :

$\tan \frac{t}{2}$ $-\tan \frac{t}{2}$ $-\cot \frac{t}{2}$ None of these

$-\cot \frac{t}{2}$

$\frac{d y}{d x}=\frac{\frac{d y}{d t}}{\frac{d x}{d t}}=\frac{-a \sin t}{a(1-\cos t)}$ $=\frac{-2 a \sin \frac{t}{2} \cos \frac{t}{2}}{2 a \sin ^2 \frac{t}{2}}=-\cot \frac{t}{2}$ Hence (3) is correct answer.