已知函数f（x）=4cosxsin（x+π/6）+3求f（x）的最小正周期

Question

已知函数f（x）=4cosxsin（x+π/6）+3
求f（x）的最小正周期

Answer 1

f(x)=4cosx(sinxcosπ/6+cosxsinπ/6)+3
=2√3sinxcosx+2cos²x+3
=√3sin2x+cos2x+4
=2(sin2x*√3/2+cos2x*1/2)+4
=2(sin2xcosπ/6+cos2x*sinπ/6)+4
=2sin(2x+π/6)+4
所以T=2π/2=π