# How do you prove that sec xcot x = csc x?

May 13, 2018

See below

#### Explanation:

We will use the following identities

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

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

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

Proof

$\sec x \cot x = \frac{1}{\cancel{\cos}} x \cancel{\cos} \frac{x}{\sin} x = \frac{1}{\sin} x = \csc x$ $\textcolor{w h i t e}{a a a a a a a a a a a a} \square$