sin2α+cos2β
=sin2α+sin(π/2-2β)
=2[sin(2α+π/2-2β)/2cos(2α-π/2+2β)/2]
=2sin(α+π/4-β)cos(α-π/4+β)
=2sin(α-β+π/4)cos(α+β-π/4)