# How do you verify the identity 1/tanx+1/cotx=tanx+cotx?

Jan 6, 2017

This is mostly just a definition question.

#### Explanation:

By definition:
$\textcolor{w h i t e}{\text{XXX}} \textcolor{red}{\cot \left(x\right) = \frac{1}{\tan \left(x\right)}}$ and $\textcolor{b l u e}{\tan \left(x\right) = \frac{1}{\cot} \left(x\right)}$

$L . S . = \textcolor{red}{\frac{1}{\tan \left(x\right)}} + \textcolor{b l u e}{\frac{1}{\cot \left(x\right)}}$

$\textcolor{w h i t e}{\text{XXX}} = \textcolor{red}{\cot \left(x\right)} + \textcolor{b l u e}{\tan \left(x\right)}$

$\textcolor{w h i t e}{\text{XXX}} = \textcolor{b l u e}{\tan \left(x\right)} + \textcolor{red}{\cot \left(x\right)}$

$\textcolor{w h i t e}{\text{XXX}} = R . S .$