Question

sinα+cosβ=1/5,cosα+sinβ=1/3,求sin(α+β)=

Answer 1

sinα+cosβ=1/5,

(sinα+cosβ)^2=1/25,

(sinα)^2+(cosβ)^2+2sinαcosβ=1/25,∵(sinα)^2+(cosβ)^2=1

∴ 2sinαcosβ=-24/25,sinαcosβ=-12/25

cosα+sinβ=1/3,

2cosαsinβ=-8/9,cosαsinβ=-4/9

sin(α+β)=sinαcosβ+cosαsinβ=-4/9-12/25=-208/225