已知函数f(x)=2cos^2x +2√3sinxcosx +a

f(x)=2cos^2x +2√3sinxcosx +a =cos2x+√3sin2x+a+1
=2cos(2x-π/3)+a+1
y=f(x+φ)=2cos(2x-π/3+2φ)+a+1
函数f(x+φ)是偶函数,-π/3+2φ=kπ;φ=(3k+1)π/6∈(0,π/2)
φ=π/6