Question

If \( x = a\left\{ \cos t + \frac{1}{2}\log\!\left(\tan^2\frac{t}{2}\right) \right\} \) and \( y = a\sin t \), then \( \frac{dy}{dx} = \) __________.

• A. \( \frac{a^2\cos^3 t}{\sin t} \)
• B. \( \tan t \)
• C. \( a\tan t \sec t \)
• D. \( \sec^2 t \)

Hint:

For parametric equations, always use \( \frac{dy}{dx}=\frac{dy/dt}{dx/dt} \)Differentiate both variables with respect to the parameter first.

Answer 1

The Correct Option is B