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

α,β∈(3/4π,π),sin(α+β)=-3/5,sin(β-π/4)+12/13cos(a+b)=4/5,cos(b-pai/4)=5/13cos(α+π/4)＝cos(a+b-(b-pai/4)=cos(a+b)c0s(b-pai/4)+sin(a+b)sin(b-pai/4)=4/5*5/13-(-3/5)*(12/13)=56/65