Question

If x = ${\displaystyle a[\cos \theta +\log \tan \frac{\theta }{2}]}$, y = asinθ then ${\displaystyle \frac{dy}{dx}}$ = ______.

विकल्प

• cosθ

• sinθ

• tanθ

• cosecθ

Answer 1

If x = ${\displaystyle a[\cos \theta +\log \tan \frac{\theta }{2}]}$, y = asinθ then ${\displaystyle \frac{dy}{dx}}$ = tanθ.

Explanation:

${\displaystyle \frac{dy}{dx}=\frac{a\cos \theta }{-a\sin \theta +\frac{a{\sec }^2 \frac{\theta }{2}}{\tan \frac{\theta }{2}}\times \frac{1}{2}}}$

= ${\displaystyle \frac{a\cos \theta }{-a\sin \theta +\frac{a}{2\cos \frac{\theta }{2}\sin \frac{\theta }{2}}}}$

= ${\displaystyle \frac{a\cos \theta }{\frac{a}{\sin \theta }-a\sin \theta }}$

= ${\displaystyle \frac{a\cos \theta \sin \theta }{a-a{\sin }^2\theta }}$

= ${\displaystyle \frac{\cos \theta \sin \theta }{{\cos }^2\theta }}$

= tanθ