# How do you verify the identity cos(pi/2-x)/sin(pi/2-x)=tanx?

Feb 6, 2017

Since

$\cos \left(\frac{\pi}{2} - \alpha\right) = \sin \alpha$

and

$\sin \left(\frac{\pi}{2} - \alpha\right) = \cos \alpha$,

you get:

$\cos \frac{\frac{\pi}{2} - x}{\sin} \left(\frac{\pi}{2} - x\right) = \sin \frac{x}{\cos} x = \tan x$