Giải thích các bước giải:
Ta có :
$\begin{split}\dfrac{\tan x+1}{\tan x-1}&=\dfrac{\dfrac{\sin x}{\cos x}+1}{\dfrac{\sin x}{\cos x}-1}\\&=\dfrac{\dfrac{\sin x+\cos x}{\cos x}}{\dfrac{\sin x-\cos x}{\cos x}}\\&=\dfrac{\sin x+\cos x}{\sin x-\cos x}\\&=\dfrac{(\sin x+\cos x)^2}{(\sin x-\cos x)(\sin x+\cos x)}\\&=\dfrac{1+2\sin x.\cos x}{\sin^2 x-\cos^2 x}\end{split}$