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
答
3pai/2cos(a+b)=4/5
pai/2cos(b-pai/4)=5/13
cos(a+pai/4)=cos[(a+b)-(b-pai/4)]
=cos(a+b)cos(b-pai/4)+sin(a+b)sin(b-pai/4)
=4/5*5/13-3/5*12/13
=-16/65
答
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
