# Math Help - Help with simplifying trigonometric identities.

1. ## Help with simplifying trigonometric identities.

I need help simplifying this:

tanX(cosX-cotX)

2. Hi Andrew Jensen

Try :

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

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

3. Hello, Andrew Jensen!

I must assume that you know some basic identities . . .

Simplify: . $\tan x(\cos x - \cot x)$

Multiply: . $\tan x\!\cdot\!\cos x - \tan x\!\cdot\!\cot x$

We know that: . $\tan x \,=\,\frac{\sin x}{\cos x} \qquad \cot x \,=\,\frac{1}{\tan x}$

So we have: . $\frac{\sin x}{{\color{red}\rlap{/////}}\cos x}\cdot{\color{red}\rlap{/////}}\cos x \;-\; {\color{red}\rlap{/////}}\tan x\cdot\frac{1}{{\color{red}\rlap{/////}}\tan x} \;\;=\;\;\sin x - 1$