Question

If $x=a(\cos \theta +log\tan \frac{\theta }{2})$ and $y=a\sin \theta$, then$\frac{dy}{dx}$ is equal to

• A. $\cot \theta$
• B. $\tan \theta$
• C. $\sin \theta$
• D. $\cos \theta$

Answer 1

The correct option is A $\cot \theta$

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

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

$=a(-\sin \theta +\frac{1}{\sin \theta })$

$y=a\left(sin\theta \right)$

$\frac{dy}{d\theta }$$=a\left(cos\theta \right)$

$\frac{dy}{dx}=\frac{\frac{dy}{d\theta }}{\frac{dx}{d\theta }}$

$=\frac{a\sin \theta }{-a(\sin \theta -\frac{1}{\sin \theta })}$

$=\frac{\sin \theta }{\cos \theta }$

$=\tan \theta$