I need help simplifying this:
tanX(cosX-cotX)
Hello, Andrew Jensen!
I must assume that you know some basic identities . . .
Simplify: .$\displaystyle \tan x(\cos x - \cot x)$
Multiply: .$\displaystyle \tan x\!\cdot\!\cos x - \tan x\!\cdot\!\cot x$
We know that: .$\displaystyle \tan x \,=\,\frac{\sin x}{\cos x} \qquad \cot x \,=\,\frac{1}{\tan x}$
So we have: .$\displaystyle \frac{\sin x}{{\color{red}\rlap{/////}}\cos x}\cdot{\color{red}\rlap{/////}}\cos x \;-\; {\color{red}\rlap{/////}}\tan x\cdot\frac{1}{{\color{red}\rlap{/////}}\tan x} \;\;=\;\;\sin x - 1$