# How do you simplify the expression secxtanxcosx?

Oct 29, 2016

$\sec x \tan x \cos x$ simplifies to $\tan x$.

#### Explanation:

Recall that $\sec x = \frac{1}{\cos x}$. We will begin by rearranging the factors so that $\sec x$ and $\cos x$ are beside each other and then proceed with substituting the definition for $\sec x$.

$\sec x \tan x \cos x$
$\tan x \sec x \cos x$
$\tan x \left(\frac{1}{\cos x}\right) \cos x$
$\tan x \left(\frac{\cos x}{\cos x}\right)$
$\tan x \left(1\right)$
$\tan x$