函数y=根号3 cos²x+sin x cos x-根号3/2的周期是?

y=根号3 cos²x+sin x cos x-根号3/2
=√3（1/2cos2x+1/2)+1/2sin2x-√3/2
=√3/2cos2x+√3/2+1/2sin2x-√3/2
=√3/2cos2x+1/2sin2x
=sinπ /3cos2x+cosπ /3sin2x
=sin(2x+π /3)
所以周期=2π /2=π