15: Factoring leads to

The fact that the fractions inside give zero follows from the scale of powers and can be confirmed using the l'Hospital rule, the geometric sequence was also used there (and the fact that |3/4| < 1).

Do not forget to substitute this answer back to the cosine.

If you decided to go the l'Hospital way, you should get

Not very nice, more applications of l'Hospital would not help either.

Answer