# Prove $\frac{\tan\theta}{1-\cot\theta}+\frac{\cot\theta}{1-\tan\theta}=\sec \theta\csc\theta+1$ [duplicate]

I did it by converting every trigonometry stuff into ${\sin}$ and $\cos$. But I want to know if there is a shortcut (without converting everything to $\sin$ and $\cos$) to do this. Please help.