Solving Basic Limit Question: Cos^2x-1/x^2

[d.tran103]

I'm stuck on this one problem:
lim (x=>0) cos^2x-1/x^2

I know the answer is -1, however I'm having trouble getting there.

Can anyone help me with this? I know cos^2x-1 is also -sin^2x and I'm having trouble with getting rid of the denominator. Thanks!

 

[micromass]

So you know the following limit??

$$\lim_{x\rightarrow 0}{\frac{\sin(x)}{x}}$$

??

If you don't know it, then you can calculate it with l'hospital's rule. This limit will help you with the limit in the OP...