已知α∈(π/2,π),β∈(π/2,3π/2),sinα=2√2/3,sinβ=7/9,则cos(α-β)=

Question

已知α∈(π/2,π),β∈(π/2,3π/2),sinα=2√2/3,sinβ=7/9,则cos(α-β)=

Answer 1

因为α∈(π/2,π),sinα=2√2/3,所以cosα=-1/3
因为),β∈(π/2,3π/2),sinβ=7/9所以cosβ=-4√2/9
cos(α-β)= cosαcosβ＋sinαsinβ =2√2/3