Problems with a trig limit (possibly involving l'hopitals)

Hi, I need to find the limit as x->0 of 1/(1-Cosx)-2/x^{2} (I know it's 1/6, but I need to figure out how to get there).

I think I need to make use of the limits (all as x->0) sinx/x=1, tanx/x=1, and (1-cosx)/x=0.

So far, I've tried multiplying the 1/((1-cosx) term by it's conjugate (1+cosx)/(1+cosx) and combined the fractions, but this hasn't really gotten me anywhere useful yet. I've also tried using l'hopitals, but the limit just gets uglier and uglier with each application. Any ideas?

Re: Problems with a trig limit (possibly involving l'hopitals)

Re: Problems with a trig limit (possibly involving l'hopitals)

While that does answer my question, I was hoping for something a bit more eloquent, that would be quite a bit of integrals to work through. But thanks for the link, I wasn't aware that Wolfram Alpha could show you it's steps. That'll definitely come in handy in the future.