# How do you determine graphically and analytically whether y_1=sinxsecx is equivalent to y_2=tanx?

Feb 13, 2018

See below.

#### Explanation:

Identitites

$\textcolor{red}{\boldsymbol{\sec x = \frac{1}{\cos} x}}$

$\textcolor{red}{\boldsymbol{\tan x = \sin \frac{x}{\cos} x}}$

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

The graph of $\boldsymbol{\sin x \sec x}$ will be identical to the graph of $\boldsymbol{\tan} x$.
We have just proved that:

$\sin x \sec x \equiv \tan x$