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

$\tan \frac{t}{2}$

$\frac{d x}{d t}=a(1+\cos t), \frac{d y}{d t}=a \sin t$

$\frac{d y}{d x}=\frac{d y}{d x} . \frac{d t}{d x}=\frac{a \sin t}{a(1+\cos t)}$

$=\frac{2 \sin \frac{t}{2} \cos \frac{t}{2}}{2 \cos ^2 \frac{t}{2}}=\tan \frac{t}{2}$

Hence (1) is correct answer.