sinα+sinβ=3/5,则(sinα+sinβ)^2=9/25,即(sinα)^2+(sinβ)^2+2sinαsinβ=9/25,同理
cosα+cosβ=4/5,则(cosα+cosβ)^2=16/25,即(cosα)^2+(cosβ)^2+2cosαcosβ=16/25
两式相加
(sinα)^2+(cosα)^2+(sinβ)^2+(cosβ)^2+2sinαsinβ+2cosαcosβ = 9/25+16/25 =1
2+2sinαsinβ+2cosαcosβ=1,即2(sinαsinβ+cosαcosβ)= -1
即sinαsinβ+cosαcosβ = cos(α-β)= -1/2