已知函数f(x)=根号3sin2x+cos(2x+π/3)+cos(2x-π/3)-1,求函数的周期
问题描述:
已知函数f(x)=根号3sin2x+cos(2x+π/3)+cos(2x-π/3)-1,求函数的周期
答
∵f(x)=√3sin2x+cos(2x+π/3)+cos(2x-π/3)-1=√3sin2x+cos2xcos(π/3)-sin2xsin(π/3)+cos2xcos(π/3)+sin2xsin(π/3)-1=√3sin2x+cos2x-1=2[(√3/2)sin2x+(1/2)cos2x]-1=2[sin2xcos(π/6)+sin(π/6)cos2x]-1=2sin...