Question

Prove that (sinθ-cosθ)^2(sinθ+cosθ)^2 = 2​

Answer 1

Explanation:

(sinθ + cosθ)^2 + (sinθ − cosθ)^2

= (sin^2 θ + cos^2 θ + 2sinθ cosθ)+(sin^2 θ+cos^2 θ − 2sinθ cosθ)

= (1 + 2sinθ cosθ) + (1 − 2sinθ cosθ)

= 1 + 2sinθ cosθ + 1 − 2sinθ cosθ

= 1 + 1 = 2

Therefore, (sinθ+cosθ)^2 + (sinθ−cosθ)^2 = 2