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

cos（α+β)=cos（(α+π/4)+(β-π/4))=cos(α+π/4)cos（β-π/4)-SIN(α+π/4)SIN（β-π/4)=4/5
sin（α+β)=sin（(α+π/4)+(β-π/4))=sin(α+π/4)cos（β-π/4)+cos(α+π/4)SIN（β-π/4)=-3/5
(IV象限)
COS(β-π/4)=-5/13(II象限)
cos(α+π/4)(-5/13)-SIN(α+π/4)(12/13)=4/5
sin(α+π/4)(-5/13)+cos(α+π/4)(12/13)=-3/5
cos(α+π/4)=-56/65