Question

Prove the identity
(cot x sin x)(sec x – cos x) = sin^2x

Answer 1

[(cosx/sinx)(sinx)][(1/cosx) - cosx]

(cosx)[(1 - cos²x)/cosx]

1 - cos²x

sin²x

Answer 2

Explanation:

`(cot x \: sinx)(secx - cosx) = {sin}^(2) x \\ \\ lhs = (cot x \: sinx)(secx - cosx) \\ = (cot x \: sinx) * secx \\- (cot x \: sinx) * cosx \\ \\ = (cosx)/(sinx) * sinx * secx\\ - (cosx)/(sinx) * sinx * cosx \\ = cosx * secx - cosx * cosx \\ = 1 - {cos}^(2) x \\ = {sin}^(2) x \\ = rhs \\ hence \: proved`