2sin(x-π/4)sin(x+π/4)=(sinx-cosx)(sinx+cosx)=-cos2a而我做的2sin(x-π/4)sin(x+π/4)=2cos(x+π/4)sin(x+π/4)=sin(2x+π/2)=cos2a差个符号?

来源:学生作业学帮网 编辑:学帮网 时间:2024/06/15 11:15:42

2sin(x-π/4)sin(x+π/4)=(sinx-cosx)(sinx+cosx)=-cos2a
而我做的2sin(x-π/4)sin(x+π/4)=2cos(x+π/4)sin(x+π/4)=sin(2x+π/2)=cos2a
差个符号?

要用这个公式,你用错了
cos(π/2+a)=-sina
sina=-cos(π/2+a)
2sin(x-π/4)sin(x+π/4)
=-2cos[π/2+(x-π/4)]sin(x+π/4)
=-2cos(x+π/4)sin(x+π/4)
=-sin(2x+π/2)
=-cos2x