Given: sinα+sinβ+sinγ=0 and cosα+cosβ+cosγ=0 sinα+sinβ+sinγ=0 ⇒sinα+sinβ=−sinγ Sqauring both sides, we get ⇒sin2α+sin2β+2sinαsinβ=sin2γ .........(1) And cosα+cosβ+cosγ=0 ⇒cosα+cosβ=−cosγ Sqauring both sides, we get ⇒cos2α+cos2β+2cosαcosβ=cos2γ ......(2) Adding (1) and (2) we get: 2+2(cosαcosβ+sinαsinβ)=1 ⇒2+2cos(α−β)=1 ⇒cos(α−β)=−