Question

已知:cos(α+β)=-3/5,cosα=5/13,且α,β∈(0,π/2)求sinβ的值

Answer 1

解：α,β∈(0,π/2) α+β∈(0,π) cos(α+β)=-3/5 sin(α+β)=4/5
cosα=5/13 sinα=12/13
sinβ=sin[(α+β)-α]=sin[(α+β)cosα-cos(α+β) sinα
=4/5x5/13+3/5x12/13
=56/65

Answer 2

α∈(0,π/2)
cosα=5/13
sinα=12/13
α,β∈(0,π/2)
α+β∈(0,π)
cos(α+β)=-3/5
sin(α+β)=4/5

sinβ
=sin[(α+β)-α]
=sin(α+β)cosα-cos(α+β)sinα
=4/5*5/13-(-3/5)*12/13
=20/65+36/65
=56/65