I'm stumped on this one for two reasons. (1) I don't see any trigonometric identities that would be convenient to help evaluate the limit, and (2) when I transformed the expression in terms of sine and cosine (to make apparent the properties of limits), it doesn't seem to work either.
Here's what I've done:
If I attempted to use properties of limits to evaluate the expression in parts, but it's not very useful unless I could do something about the denominator:
Even if I do say so, we had a great success with the numbers of students went on to the PhD or MD from those classes.
So I say: never use the L'Hopital's rule if it can be avoided.