已知α,β属于(3π/4,π),sin(α+β)=-3/5,sin(β-π/4)=12/13,求cos(α+π/4)

已知α,β属于(3π/4,π),sin(α+β)=-3/5,sin(β-π/4)=12/13,求cos(α+π/4)
已知α,β属于(3π/4,π),sin(α+β)=-3/5,sin(β-π/4)=12/13,求cos(α+π/4)

已知α,β属于(3π/4,π),sin(α+β)=-3/5,sin(β-π/4)=12/13,求cos(α+π/4)
α,β∈(3π/4,π),
则α+β∈(3π/2,2π),β-π/4∈(π/2,3π/4)
∴cos(α+β)>0,cos(β-π/4)