已知函数f(x)=2sinxcos(x+π/3)+根号3cos的平方x+1/2sin2x求函数f的最小正周期

问题描述:

已知函数f(x)=2sinxcos(x+π/3)+根号3cos的平方x+1/2sin2x求函数f的最小正周期

解原式=2sinxcos(x+π/3)+根号3cos的平方x+1/2sin2x=2sinxcos(x+π/3)+根号3cos的平方x+sinxcosx=2sinxcos(x+π/3)+cosx(根号3cosx+sinx=2sinxcos(x+π/3)+2cosxsin(x+π/3)=2sin[x+(x+π/3)]=2sin(2x+π/3)所以周期为2π/2=π