Question

Pls help sin(x)/1- cos(x) - cot(x) = csc(x)​

Answer 1

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