Question

Prove Tan x - 1/Tan x + 1 = 1 - cot x/1 + cot x

Answer 1

$\dfrac{\tan x-1}{\tan x+1}=\dfrac{\dfrac{\sin x}{\cos x}-1}{\dfrac{\sin x}{\cos x}+1}=\dfrac{\sin x-\cos x}{\sin x+\cos x}=\dfrac{1-\dfrac{\cos x}{\sin x}}{1+\dfrac{\cos x}{\sin x}}=\dfrac{1-\cot x}{1+\cot x}$