It looks like:
We can use L'Hôpital's Rule because this is in indeterminate form, ie if we plug the x-value straight in, we get
So after one round of L'Hôpital, we are at:
If we plug the x-value straight in again, we get:
Of course, that's a complete black-box. The more transparent way is to use, perhaps, a Taylor Expansion; or, maybe some algebraic manipulation of the trig functions.