tanα=4/3,sin(α+β)=5/13,α∈(0,π/2),β∈(π/2,π) 求sinβ

题目

tanα=4/3,sin(α+β)=5/13,α∈(0,π/2),β∈(π/2,π) 求sinβ

答案

α∈(0,π/2),
sinα=4/5
cosα=3/5
sin(α+β)=5/13
cos(α+β)=-12/13
sinβ=sin(α+β-α)=5/13*3/5-(-12/13)*4/5
=15/65+48/64
=63/64