设 A=α+β,B=β-α,
则 2α=A-B,2β=A+B
所以 cos2α-cos2β=cos(A-B)-cos(A+B)
=cosAcosB+sinAsinB-( cosAcosB-sinAsinB )
=2sinAsinB
=2sin(α+β)sin(β-α)