已知a,b,属于(3pi/4,pi),sin(a+b)=-3/5,sin(b-pi/4)=12/13,则cos(a+pi/4)=?
问题描述:
已知a,b,属于(3pi/4,pi),sin(a+b)=-3/5,sin(b-pi/4)=12/13,则cos(a+pi/4)=?
答
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.