# Question #7e3cb

Apr 15, 2017

$\sin x \tan x$

#### Explanation:

An important fact to note here is that:
${\sin}^{2} x + {\cos}^{2} x = 1$
Therefore:
${\sin}^{2} x = 1 - {\cos}^{2} x$

So if we put this into the equation given:
$\frac{1 - {\cos}^{2} x}{\cos} x = {\sin}^{2} \frac{x}{\cos} x$
$= \sin x \cdot \sin \frac{x}{\cos} x$
$= \sin x \cdot \tan x$

If you need explanation as to why ${\sin}^{2} x + {\cos}^{2} x = 1$, please comment below