At this point, I can't use L'Hopital's rule. I tried to solve this using two different approaches and continue to get a 0 in the denominator even though I know that 0 should cancel out somehow. Here's the exercise:

Use the definition of the derivative to show that d/dx[cos x] = -sin x.

Hint: Use the limit laws in section 1.6 and the identity cos (A + B) = cos A cos B - sin A sin B.

Please help. This is one of two problems that I have left to do and have spent lots of time trying to solve to no avail.