这题应该不用和差化积、积化和差之类的.
cosα+cosβ=0
则cosα=-cosβ
α=(2k+1)π-β k∈Z
而sinα=sin[(2k+1)π-β]=sinβ
又sinα+sinβ=1
sinα=sinβ=1/2
cos2α=1-2(sinα)^2=1-2(sinβ)^2=cos2β=1/2
cos2α+cos2β=1