sin2x(2cos2x-1)=cos2x(√3-2sin2x)
2sin2xcos2x-sin2x=√3cos2x-2sin2xcos2x
4sin2xcos2x=√3cos2x+sin2x
2sin4x=2(√3/2*cos2x+1/2*sin2x)
sin4x=(sinπ/3*cos2x+cosπ/3*sin2x)
sin4x=sin(π/3+2x)
4x=2kπ+π/3+2x 或4x=2kπ+π-(π/3+2x)
由4x=2kπ+π/3+2x得
x=kπ+π/6
k=0时,x=π/6;k=1时,x=7π/6;k=2时,x不在[0,2π)内,所以不考虑
由4x=2kπ+π-(π/3+2x)得
x=kπ/3+π/9
k=0时,x=π/9;k=1时,x=4π/9;k=2时,x=7π/9;k=3时,x=10π/9;k=4时,x=14π/9;k=5时,x=17π/9,k=6时,x不在[0,2π)内,所以不考虑
所以x值可为π/9,π/6,4π/9,7π/9,10π/9,7π/6,14π/9,17π/9