191问答库 > 已知a,b属于(3π⼀4,π),sin(a+b)=-3⼀5,sin(b-π⼀4）=12⼀13，则cos(a+π⼀4)=?

已知a,b属于(3π⼀4,π),sin(a+b)=-3⼀5,sin(b-π⼀4）=12⼀13，则cos(a+π⼀4)=?

2025-04-06 23:40:24

推荐回答（2个）

回答1：

a+b 属于(3/2π,2π) cos(a+b)=4/5 b-π/4 属于(1/2π,3/4π) cos(b-π/4)=-5/13
cos(a+π/4)=cos(a+b)cos(b-π/4)-sin(a+b)*sin(b-π/4)=4/5*-5/13-(-3/5)*12/13=(36-20)/65=16/65
望采纳哦

回答2：

a,b属于(3π/4,π),
a+b属于(3π/2,2π)
sin(a+b)=-3/5
cos(a+b)=4/5

b-π/4属于(π/2,3π/4)
sin(b-π/4）=12/13
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
=-56/65