Question

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

Answer 1

Step-by-step explanation:

$(cot x \: sinx)(secx - cosx) = {sin}^{2} x \\ \\ lhs = (cot x \: sinx)(secx - cosx) \\ = (cot x \: sinx) \times secx \\- (cot x \: sinx) \times cosx \\ \\ = \frac{cosx}{sinx} \times sinx \times secx\\ - \frac{cosx}{sinx} \times sinx \times cosx \\ = cosx \times secx - cosx \times cosx \\ = 1 - {cos}^{2} x \\ = {sin}^{2} x \\ = rhs \\ hence \: proved$

Answer 2

Answer:

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

(cosx)[(1 - cos²x)/cosx]

1 - cos²x

sin²x