sinA-cosA=√2/2
(sinA-cosA)^2 = 1/2
sin^2A+cos^2A-2sinAcosA = 1/2
1-sin2A = 1/2
sin2A = 1/2
cos4A = 1 - 2sin^2(2A) = 1-2*(1/2)^2 = 1/2