# How do you verify secx-cosx=sinx/cotx?

Apr 24, 2016

Use the following identities:

#### Explanation:

$\sec x = \frac{1}{\cos} x$

$\cot x = \cos \frac{x}{\sin} x$

$\frac{1}{\cos} x - \cos x = \sin \frac{x}{\cos \frac{x}{\sin} x}$

$\frac{1 - \left(\cos x\right) \left(\cos x\right)}{\cos} x = \frac{\left(\sin x\right) \left(\sin x\right)}{\cos} x$

Applying the pythagorean identity $1 - {\cos}^{2} x = {\sin}^{2} x$:

${\sin}^{2} \frac{x}{\cos} x = {\sin}^{2} \frac{x}{\cos} x$