大师作文网sin2x=sin(x-派/3)和cos(2x-派/6)=sin(3x-派/3)和sin5x=sin3x这种方程怎么解啊
来源：学生作业帮 编辑：大师作文网作业帮 分类：数学作业 时间：2024/11/13 01:55:14
sin2x=sin(x-派/3)和cos(2x-派/6)=sin(3x-派/3)和sin5x=sin3x这种方程怎么解啊
1.sin2x=sin(x-π/3)
则2x=2kπ+(x-π/3)或2x=π-(2kπ-π/3)+2kπ
所以x=2kπ-π/3 或x=4π/9+2kπ/3
2.cos(2x-π/6)=sin(3x-π/3)
sin(π/2-(2x-π/6))=sin(3x-π/3)
sin(2π/3-2x)=sin(3x-π/3)
则2π/3-2x=2kπ+(3x-π/3）或2π/3-2x=π-(3x-π/3)+2kπ
所以化简：x=(1-2kπ)/5或x=2kπ+π/3
3.5x=2kπ+3x或5x=π-3x+2kπ
x=kπ或x=π/8+kπ/4
则2x=2kπ+(x-π/3)或2x=π-(2kπ-π/3)+2kπ
所以x=2kπ-π/3 或x=4π/9+2kπ/3
2.cos(2x-π/6)=sin(3x-π/3)
sin(π/2-(2x-π/6))=sin(3x-π/3)
sin(2π/3-2x)=sin(3x-π/3)
则2π/3-2x=2kπ+(3x-π/3）或2π/3-2x=π-(3x-π/3)+2kπ
所以化简：x=(1-2kπ)/5或x=2kπ+π/3
3.5x=2kπ+3x或5x=π-3x+2kπ
x=kπ或x=π/8+kπ/4
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