已知函数f(x)=2cosxsin(x+π/3)-√3sin^2x+sinxcosx,向右平移m个单位（m>0)使函数为偶函数,求m的最小值

题目

已知函数f(x)=2cosxsin(x+π/3)-√3sin^2x+sinxcosx,向右平移m个单位（m>0)使函数为偶函数,求m的最小值

答案

f(x)=2cosxsin(x+π/3)-√3sin^2x+sinxcosx=2cosx(sinx*1/2+cosx*sqrt(3)/2)-sqrt(3)sin^2(x)+sinxcosx=2sinxcosx+sqrt(cos^2(x)-sin^2(x))=sin2x+sqrt(3)cos2x=2(cosπ/3 sin2x+ sin π/3 cos2x)=2sin(2x+π/3)= 2s...