sin(α+β)cosβ-cos(α+β)sinβ= sin[(α+β)-β] = sinα = 0 则,
sin(α+2β)+sin(α-2β)
=[sinα*cos(2β) + cosα*sin(2β)] + [sinα*cos(2β) - cosα*sin(2β)]
=2sinα*cos(2β)
=2*0*cos(2β)
=0