Q:

Trig identity confusion $\cos x\tan^2(x)$

How come $\cos x\tan^2(x)$ can be changed to $\sec x\sin^2(x)$ ? What are the steps?

A:

$\displaystyle \cos(x)\cdot \tan^2(x)= \cos(x)\cdot \frac{sin^2(x)}{cos^2(x)}=\frac{sin^2(x)}{cos(x)}=sec(x)\cdot sin^2(x)$

