UC知道sin(a+b)=-3/5,sin(b-π/4）=12/13，求cos（a+π/4)值
来源：百度知道 编辑：UC知道 时间：2024/09/24 09:19:05
cos（a+π/4)
=cos[(a+b)-(b-π/4)]
=cos(a+b)cos(b-π/4)+sin(a+b)sin(b-π/4)
又sin(a+b)=-3/5,sin(b-π/4）=12/13，
所以cos(a+b)=4/5(a+b为第四象限角),cos(a+b)=4/5(a+b为第四象限角)
cos(b-π/4)=5/13(b-π/4为第一象限角),cos(b-π/4)=-5/13(b-π/4为第二象限角)，
所以cos（a+π/4)=-16/65，-56/65
sin(a+b)=-3/5,cos(a+b)=4/5,或-4/5
sin(b-π/4）=12/13,cos(b-π/4)=5/13,或-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)
cos(a+b)与cos(b-π/4)同号时（同正或同负）
=20/65-36/65=-16/65
cos(a+b)与cos(b-π/4)异号时（一正一负）
=-20/65-36/65=-56/65
sin(a+b)=-3/5
则cos(a+b)=4/5或(-4/5)
sin(b-π/4)=12/13
则cos(b-π/4)=5/13或(-5/13)
所以
cos(a+π/4)
=cos[(a+b)-(b-π/4)]
=cos(a+b)*cos(b-π/4)+sin(a+b)*sin(b-π/4)
=cos(a+b)*cos(b-π/4)-36/65
当cos(a+b)与cos(b-π/4)同号时(同正或同负)
cos(a+b)*cos(b-π/4)=20/65
cos(a+π/4)=-16/65
当cos(a+b)与cos(b-π/4)异号时(一正一负)
cos(a+b)*cos(b-π/4)=-20/65
cos(a+π/4)=-56/65
sin(a+b)=-