# How do you verify sec^2 x/ tan x = sec x csc x?

Jul 31, 2015

By using the following rules :
$\sec x = \frac{1}{\cos} x$

$\csc x = \frac{1}{\sin} x$

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

#### Explanation:

Required to prove : ${\sec}^{2} \frac{x}{\tan} x = \sec x \csc x$

Starting from the Left Hand Side of the equation

$\text{LHS} = {\sec}^{2} \frac{x}{\tan} x$

$= {\left(\sec x\right)}^{2} / \tan x$

$= {\left(\frac{1}{\cos} x\right)}^{2} / \left(\sin \frac{x}{\cos} x\right)$

=1/(cosx)^2÷(sinx/cosx)

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

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

=color(blue)(secxcscx

$\text{QED}$