已知函数f(x)=2cosxsin(x+60°)-根号3sin^2x+sinxcosx

题目

已知函数f(x)=2cosxsin(x+60°)-根号3sin^2x+sinxcosx
求f(x)的最小正周期

答案

f(x)=2cosxsin(x+60°)-√3sin²x+sinxcosx
=2cosx(sinxcos60º+cosxsin60º)-√3sin²x+sinxcosx
=sinxcosx+√3cos²x-√3sin²x+sinxcosx
=2sinxcosx+√3(cos²x-sin²x)
=sin2x+√3cos2x
=2(1/2sin2x+√3/2cos2x)
=2sin(2x+π/3)
f(x)的最小正周期 T=2π/2=π