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

题目

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

答案

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