Question

tana=-1/3,cos(a+b)=-12/13,a,b属于(π/2,π)

Answer 1

α∈(π/2,π),tanα=-1/3,则sinα=1/√10,cosα=-3/√10

α+β∈(π,2π),cos(α+β)=-12/13,则sin(α+β)=-5/13

cosβ＝cos(α+β-α)＝cos(α+β)cosα＋sin(α+β)sinα＝-12/13×(-3/√10)＋(-5/13)×1/√10＝31/(13√10)