I've been trying to work out this limit problem for the past few days. I got a few friends to look at it, and they haven't been able to solve it either. I think I'm just overlooking something...but I'm almost positive I need to apply the cosine double angle identity...I just get stuck after that. Here's the problem:

lim cos(2x) - cos(x)

x->0 ----------------

x

I just can't figure out how to evaluate it. Any help would be appreciated.