[tex]\LARGE\begin{aligned}&\left(\dfrac{1}{\sin x}-\dfrac{1}{\cos x}\right)(\sin x+\cos x)=\cot x -\tan x\\ &\dfrac{\sin x+\cos x}{\sin x}-\dfrac{\sin x+\cos x}{\cos x}=\cot x -\tan x\\ &\dfrac{\sin x}{\sin x}+\dfrac{\cos x}{\sin x}-\dfrac{\sin x}{\cos x}-\dfrac{\cos x}{\cos x}=\cot x -\tan x \\&1+\dfrac{\cos x}{\sin x}-\dfrac{\sin x}{\cos x}-1=\cot x -\tan x \\&\cot x -\tan x=\cot x -\tan x\end[/tex]
