# How do you prove (sinx + tanx) / cosx + 1 = tanx?

Jan 25, 2016

The given equation is not true and therefore can not be proven.

#### Explanation:

Consider for example the case when $x = 0$

$\textcolor{w h i t e}{\text{XXX}} \cos \left(0\right) = 1$
$\textcolor{w h i t e}{\text{XXX}} \sin \left(0\right) = 0$

So when $x = 0$
$\textcolor{w h i t e}{\text{XXX}} \frac{\sin x + \tan x}{\cos x} + 1 = \tan x + 1$
which obviously can not be equal to
$\textcolor{w h i t e}{\text{XXX}} \tan x$