作业帮 > 数学 > 作业

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

来源:学生作业帮 编辑:灵鹊做题网作业帮 分类:数学作业 时间:2024/03/29 12:50:13
a,b∈(3pi/4,pi),sin(a+b)=-3/5,sin(b-pi/4)=12/13,则cos(a+pi/4)=
a,b∈(3pi/4,pi),sin(a+b)=-3/5,sin(b-pi/4)=12/13,则cos(a+pi/4)=
解cos(a+π/4)
=cos[(a+b)-(b-π/4)]
=cos(a+b)cos(b-π/4)+sin(a+b)sin(b-π/4)
由a,b∈(3pi/4,pi),sin(a+b)=-3/5,sin(b-pi/4)=12/13
知a+b属于(3π/2,2π),b-π/4属于(π/2,3π/4)
cos(a+b)=4/5,cos(b-π/4)=5/13

cos(a+π/4)
=cos[(a+b)-(b-π/4)]
=cos(a+b)cos(b-π/4)+sin(a+b)sin(b-π/4)
=4/5*5/13+(-3/5)*(12/13)
=20/65-36/65
=-16/65