Question

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

Prove the identity.
Note that each Statement must be based on a Rule chosen from the Rule menu. To see a detailed description of a Rule, select the More Information Button to the right of the Rule.

Answer 1

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