Which period is this function?

This question is from the National University of Colombia entrance exam in 2006 (translated from Spanish).

The function y=4cos(x/2) - 3sin2x is of period:

A. π

B, 4π

C. 3π

D. 2π

I learned to divide the period of cos by 2π, so 2π/1/2 would be 4π I thought, and the period for the sin would be 2π/2 is π, and the least common number to divide into seems like it would make the answer 4π, but the answer sheet says D, 2π, and I can't figure out why. I have their entrance exam in two days and I need to understand all this. Please help me. Thank you