f(x) = cos [π / 2 - (x + π / 3)] cos [π / 2 - (x + π / 2)]
= cos (π / 6 - x) cos (-x)
= (√3 / 2 cos x + 1 / 2 sin x) cos x
= √3 / 2 (cos x)^2 + 1 / 2 sin x cos x
= √3 / 4 2 (cos x)^2 + 1 / 4 2 sin x cos x
= √3 / 4 [1 + cos (2 x)] + 1 / 4 sin (2 x)
= √3 / 4 + 1 / 2 [√3 / 2 cos (2 x) + 1 / 2 sin (2 x)
= √3 / 4 + 1 / 2 sin (2 x + π / 3)
2 π / 2 = π ,
所以,f(x)的最小正周期是 π .