# How do you verify the identity 1/(secxtanx)=cscx-sinx?

Feb 20, 2017

#### Explanation:

$\sec x \tan x$

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

= $\frac{1}{\sin \frac{x}{\cos} ^ 2 x}$

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

= $\frac{1 - {\sin}^{2} x}{\sin} x$

= $\frac{1}{\sin} x - {\sin}^{2} \frac{x}{\sin} x$

= $\csc x - \sin x$