Prove the following identities (2sin x cos x - cos x)/(1 - sin x + sin^2 x - cos^2 x) = cot x

Question

Prove the following identities

\(\cfrac{2sin\,\text x\,cos\,\text x-cos\,\text x}{1-sin\,\text x+sin^2\text x-cos^2\text x}\) = cot x

Answer 1

LHS = \(\cfrac{2sin\,\text x\,cos\,\text x-cos\,\text x}{1-sin\,\text x+sin^2\text x-cos^2\text x}\) 

We know that 1 – cos²x = sin²x

= cot x

= RHS

Hence proved.