则cos(α-γ)=

cosα+cosβ+cosγ=0,sinα+sinβ+sinγ=0 ,→

cosα+cosγ=-cosβ....................(1)

sinα+sinγ=-sinβ....................(2)

(1)平方+(2)平方:

(cosα+cosγ)^2+(sinα+sinγ)^2=1

(cosα)^2+2cosαcosγ+(cosγ)^2+(sinα)^2+2sinαsinγ+(sinγ)^2=1

2[cosαcosγ+sinαsinγ]+2=1

2cos(α-γ)=-1

∴cos(α-γ)=-1/2

标签： cos