If y = a(1 + cos t) and x = a(t – sin t), then $\frac{dy}{dx}$ is :
Answer & explanation
Correct answer: option 3
$\frac{d y}{d x}=\frac{\frac{d y}{d t}}{\frac{d x}{d t}}=\frac{-a \sin t}{a(1-\cos t)}$
$=\frac{-2 a \sin \frac{t}{2} \cos \frac{t}{2}}{2 a \sin ^2 \frac{t}{2}}=-\cot \frac{t}{2}$
Hence (3) is correct answer.