32: Putting infinity into sine and cosine does not help, since they oscillate and limit algebra cannot be used. However, they bounded, so they should not influence what eventually happens with n. Intuitive evaluation suggests that
How to prove this? One possibility is to prove that the above comparison was correct, which is done by taking the limit of the ratio of the given expression and the simpler expression at infinity and obtaining 1. However, that is some work. Somewhat easier is to show that the denominator goes to infinity (by a simple comparison) and the use l'Hospital's rule.
By far the easiest solution is to apply comparison to the whole given expression, so find a suitable lower estimate to force it up to infinity.