已知cos(派/4+x)=3/5(0<x<派/4) 1.求sin2x 2.求cos(2x+派/4)

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/29 01:26:15
已知cos(派/4+x)=3/5(0<x<派/4) 1.求sin2x 2.求cos(2x+派/4)

已知cos(派/4+x)=3/5(0<x<派/4) 1.求sin2x 2.求cos(2x+派/4)
已知cos(派/4+x)=3/5(0<x<派/4) 1.求sin2x 2.求cos(2x+派/4)

已知cos(派/4+x)=3/5(0<x<派/4) 1.求sin2x 2.求cos(2x+派/4)

1、∵ 0

∵cos(π/4+x)=3/5
∴cos(π/4)cosx+sin(π/4)sinx=3/5
∴sin2x=7/25
∵0﹤x﹤π/4 ∴0﹤x﹤π/2
∴cos2x=24/25
∴cos(2x+π/4)=cos2xcos(π/4)-sin2xsin(π/4)=17(根号2)/50