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

问题描述:

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)=4/5sin(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(...