You have missed a 'c' somewhere, thats why we will not be getting any answer correctly. But I will tell you the general idea...

Let L be the limit.

Observe that if and L, then .

Applying it here, we get .

Now apply L'Hospital's rule, to get another form for L. Do the same process again.

Alternate trick is to substitute the power series for cos and choosing coefficients such that the limit exists.