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

问题描述:

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

cos(a+π/4)=cos((a+B)-(B-π/4))=cos(a+B)cos(B-π/4)+sin(a+B)sin(B-π/4)
3π/2