Question

If $x=\cos \theta$ and $y=\tan \theta$ find $\frac{dy}{dx}$

Answer 1

$x=\cos \theta \frac{dx}{d\theta }=\frac{d}{dx}\cos \theta \frac{dx}{d\theta }=-\sin \theta y=\tan \theta \frac{dy}{d\theta }=\frac{d}{d\theta }\tan \theta \frac{dy}{d\theta }=se{c}^2\theta ⟹\frac{dy}{dx}=\frac{se{c}^2\theta }{-\sin \theta }$