已知函数f(x)=2cosxcos(x-π/6)-√3sin∧2x+sinxcosx.求f(x)的最小正周期

问题描述:

已知函数f(x)=2cosxcos(x-π/6)-√3sin∧2x+sinxcosx.求f(x)的最小正周期

首先化简f(x)=2cosxcos(x-π/6)-√3sin^2x+sinxcosx=2cosxcos(x-π/6)-2sinx(√3/2sinx-1/2cosx)=2cosxcos(x-π/6)-2sinx(sinxcosπ/6-cosxsinπ/6)=2cosxcos(x-π/6)-2sinxsin(x-π/6)=2cos(x+x-π/6)=2cos(2x-π/6...