Question

(Sinθ-cosθ)(sinθ+cosθ)=1-2cos^2θ

Answer 1

See below

Explanation:

`( \sin \theta - \cos \theta)( \sin \theta + \cos \theta) = 1 - 2 { \cos}^(2) \theta \\ \\ LHS = ( \sin \theta - \cos \theta)( \sin \theta + \cos \theta) \\ \\ = \sin^(2) \theta - \cos^(2) \theta \\ \\ =1 - \cos^(2) \theta - \cos^(2) \theta \\( \because \sin^(2) \theta =1 - \cos^(2) \theta) \\ \\ = 1 - 2 { \cos}^(2) \theta \\ = RHS`

Thus proved