Question

(sinx) / (1-cosx) =cscx+cotx

Answer 1

$~~\text{L.H.S}\\\\=\dfrac{\sin x}{1-\cos x}\\\\\\=\dfrac{\sin x(1+ \cos x)}{(1 -\cos x)(1+ \cos x)}\\\\\\=\dfrac{\sin x + \sin x \cos x}{1- \cos^2 x}\\\\\\=\dfrac{\sin x+ \sin x \cos x}{\sin^2 x}\\\\\\=\dfrac{\sin x}{ \sin^2 x}+ \dfrac{\sin x \cos x}{ \sin^2 x}\\\\\\=\dfrac{1}{ \sin x} + \dfrac{\cos x}{ \sin x}\\\\\\=\csc x + \cot x\\\\\\=\text{R.H.S}\\\\\text{Proved.}$