cos^2(α+β)+2sin(α+β)cos(α+β)-2sin^2(α+β)
设a+b=x
=cosx^2+2sinxcosx-2sinx^2
=(1+cos2x)/2+sin2x-(1-cos2x)
=sin2x+3cos2x/2-1/2
=根号2sin(2x+arctan3)-1/2
=根号2sin(2(α+β)+arctan3)-1/2