# How do you verify the identity cosx+sinxtanx=sec x?

May 1, 2015

Use the fact that:
$\tan x = \sin \frac{x}{\cos} x$
and
$\sec x - \frac{1}{\cos} x$
So:
$\cos x + \sin x \sin \frac{x}{\cos} x = \frac{1}{\cos} x$
$\frac{{\cos}^{2} x + {\sin}^{2} x}{\cos x} = \frac{1}{\cos} x$
$\frac{1}{\cos x} = \frac{1}{\cos} x$

Where I used: ${\sin}^{2} x + {\cos}^{2} x = 1$