已知阿尔法,贝塔属于(3π/4,π),sin(阿尔法+贝塔)=-3/5,sin(贝塔-π/4)=12/13,则sin(阿尔法+π/4)=
问题描述：
已知阿尔法,贝塔属于(3π/4,π),sin(阿尔法+贝塔)=-3/5,sin(贝塔-π/4)=12/13,则sin(阿尔法+π/4)=
答
a,b∈(3π/4,π)
a+b∈(3π/2,2π)
sin(a+b)=-3/5
cos(a+b)>0
cos(a+b)=4/5
b∈(3π/4,π)
b-π/4∈(π/2,3π/4)
sin(b-π/4)=12/13
cos(b-π/4)cos(b-π/4)=-5/13
sin(a+π/4)
=sin[(a+b)-(b-π/4)]
=sin(a+b)cos(b-π/4)-cos(a+b)sin(b-π/4)
=-3/5*(-5/13)-4/5*12/13
=15/65-48/65
=-33/65