已知角ab sin(a+b)=-3/5 sin(b-π/4)=12/13 求cos(a+π/4))

题目

已知角ab sin(a+b)=-3/5 sin(b-π/4)=12/13 求cos(a+π/4))

答案

由已知可知cos(a+b)=-4/5,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