cos4a=2(cos2a)²-1=2(1-2(sina)²)-1
cos4b=2(cos2b)²-1=2(1-2(sinb)²)-1
2cos4a-1/2cos4b=2*{2(1-2(1/2*(sinθ+cosθ) )²)-1}-1/2*{2(1-2(sinθcosθ))-1}
=2*{2(1-1/2*(1+sin2θ )-1}-1/2*{2(1-2(sinθcosθ))-1}
=2+2sin2θ-sin2θ
=2+sin2θ