[tex]\text{LHS}=\frac{\sin x}{1-\cos x}-\cot x\\\\=\frac{\sin x}{1-\cos x}-\frac{\cos x}{\sin x}\\\\=\frac{\sin^{2} x}{\sin x(1-\cos x)}-\frac{\cos x(1-\cos x)}{\sin x(1-\cos x)}\\\\=\frac{\sin^{2} x-\cos x(1-\cos x)}{\sin x(1-\cos x)}\\\\=\frac{\sin^{2} x-\cos x+\cos^{2} x}{\sin x(1-\cos x)}\\\\=\frac{(\sin^{2} x+\cos^{2} x)-\cos x}{\sin x(1-\cos x)}\\\\=\frac{1-\cos x}{\sin x(1-\cos x)}\\\\=\frac{1}[\sin x}\\\\=\csc x\\\\=\text{RHS}[/tex]
