Question

已知cosα=-4/5,sinβ=-3/4,α∈(π/2,π),β∈(π,3/2π),求cos(α-β)

Answer 1

cos(a-b)=cosacosb+sinasinb
因为 cosa=-4/5,sinb=-3/4,a∈(π/2,π), b∈(π,3/2π),
所以 sina=3/5,cosb=-根号7/4
所以 cos(a-b)=-(4*根号7+9)/20

Answer 2

cosα=-4/5,α∈（π/2,π）推出sinα=3/5
sinβ=-3/4,β∈(π,3/2π) 推出cosβ=-根7/4
cos(α-β)=cosαcosβ+sinαsinβ=-4根7/20-9/20