Question

(sinx+cosx)^2 + (sinx-cosx)^2 = .....

Answer 1

(sinx+cosx)² + (sinx-cosx)² = .....
⇔ sin²x + 2sinx.cosx + cos²x + sin²x - 2sinx.cosx + cos²x
⇔ 2(sin²x + cos²x)
⇔ 2(1)
⇔ 2

Answer 2

(sin x + cos x) (sin x + cos x) + (sin x - cos x)(sin x - cos x)
= (sin^2 x + 2 sin x cos x + cos^2 x) + (sin^2x -2sin x cos x + cos ^2 x)
= sin ^2x + sin ^2x + cos ^2x +cos ^2x
= sin^2x + cos^2x + sin^2 x+ cos^2x
= 1+ 1
= 2