Question

Differentiate:$x=a(\cos t+\log \tan \frac{t}{2}),y=a\sin t$

Answer 1

$x=a(\cos t+\log \tan \frac{t}{2})$

$\frac{dx}{dt}=a(-\sin t+\frac{{\sec }^2\frac{t}{2}}{2\tan \frac{t}{2}})$

$y=a\sin t$

$\frac{dy}{dt}=a\cos t$

$\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}$

$=\frac{a\cos t}{a(-\sin t+\frac{{\sec }^2\frac{t}{2}}{2\tan \frac{t}{2}})}$

$\therefore \frac{dy}{dx}=\frac{\cos t}{(-\sin t+\frac{{\sec }^2\frac{t}{2}}{2\tan \frac{t}{2}})}$