Establish the identity

Question

(Sin + cos)^2 + (sin - cos)^2 = 2

please write full answer

Answer 1

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

expand

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

cancel the 2sinxcosx terms, one is negative the other positive

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

2(sin^2(x) + cos^2(x)) = 2, cos^2(x) + sin^2(x) =1 substitute

2(1) = 2

2 = 2

Answer 2