已知函数f(x)=sinxcosx-根号3cos^2x+2分之根号3,求函数f(x)的周期和对称轴方程

Question

已知函数f(x)=sinxcosx-根号3cos^2x+2分之根号3,求函数f(x)的周期和对称轴方程

Answer 1

f(x)=2cosxsin(x+π/3)-√3sin^2x+sinxcosx
=cosx(sinx+√3cosx)-√3(sinx)^2+sinxcosx
=2sinxcosx+√3[(cosx)^2-(sinx)^2]
=sin2x+√3cos2x
=2sin(2x+π/3)=x/50π,
sin(2x+π/3)=x/100π,
由于|sin(2x+π/3)|