The fundamental period of the function $\sin(\frac{\pi[x]}{12})+\tan(\frac{\pi[x]}{3})+\cos(\frac{\pi x}{4})$ is
(A) 12
(B) 24
(C) 36
(D) function is non-periodic
(where $[\cdot]$ represents the greatest integer function)
My approach is as follows: With $N$ an integer,
$[x+N]=[x]+N$
How do I proceed from here?