# How do you verify (sec x + csc x) (sin x + cos x) – 2 – cot x tan x?

$\left(\sec x + \csc x\right) \left(\sin x + \cos x\right) = \sec x \sin x + \sec x \cos x + \csc x \sin x + \csc x \cos x$
$= \sin \frac{x}{\cos} x + \cos \frac{x}{\cos} x + \sin \frac{x}{\sin} x + \sin \frac{x}{\cos} x$
$= \tan x + 1 + 1 + \cot x$
$= \tan x + \cot x + 2$