Question

已知函数f(x)=2cosxsin(x+∏/3)-[(根号3)/2].

求函数f(x)的最小正周期.
请写出计算过程和结果好吗?

Answer 1

f(x)=2cosx(sinxcosπ/3+cosxsinπ/3)-√3/2
=sinxcosx+√3cos²x-√3/2
=1/2*sin2x+√3(1+cos2x)/2-√3/2
=1/2*sin2x+√3/2*cos2x
=sin2xcosπ/3+cos2xsinπ/3
=sin(2x+π/3)
T=2π/2=π