已知a,b,属于（3pi/4,pi),sin(a+b)=-3/5,sin(b-pi/4)=12/13,则cos(a+pi

sin(a+b)=-3/5,a,b∈（3π/4,π),
则cos(a+b)=4/5,
sin(b-π/4)=12/13,b∈（3π/4,π),
则cos(b-π/4)=-5/13.
则cos(a+π/4)= cos[(a+b) -(b-π/4)]
= cos(a+b) cos(b-π/4) +sin(a+b) sin(b-π/4)
=-56/65.