Problem: Evaluate

Solution: Since we have an expression inside a "nice" function, we can move the cosine out (or equivalently, move the limit sign into the cosine). Then we will try to substitute into the sequence, hoping that we will get an answer using the limit algebra:

Note: The part between double angled braces ⟪ and ⟫ is "unofficial". When writing something important (for instance a test), it is safer to write these notes on the side so that it is not a part of the "official" solution.