Step-by-step explanation:
[tex](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[/tex]
