(Sin(x) - Cos(x) )^2 = sin^2(x) - 2 sin(x)*cos(x) + cos^2(x) (sin(x) + cos(x) )^2 = sin^2(x) + 2sin(x)*cos(x) + cos^2(x) Add these two 2sin^2(x) + 2cos^2(x) is all that is left. The two middle terms cancel out
Take out the common factor of 2 2(sin^2(x) + cos^2(x) ) but sin^2(x) + cos^2(x) = 1
