# How do you prove Sec(x) - cos(x) = sin(x) * tan(x)?

Apr 30, 2016

I changed $\sec$ and $\tan$:

#### Explanation:

We can change the $\sec$ and $\tan$ to write:
$\frac{1}{\cos} \left(x\right) - \cos \left(x\right) = \sin \left(x\right) S \in \frac{x}{\cos} \left(x\right)$

rearranging the left and right sides:

$\frac{1 - {\cos}^{2} \left(x\right)}{\cos} \left(x\right) = {\sin}^{2} \frac{x}{\cos} \left(x\right)$

and remeber that: ${\sin}^{2} \left(x\right) = 1 - {\cos}^{2} \left(x\right)$

to write:

${\sin}^{2} \frac{x}{\cos} \left(x\right) = {\sin}^{2} \frac{x}{\cos} \left(x\right)$