The problem asks you to provide the formulas for $\cos(x + y)$ and $\cos(x - y)$ based on trigonometric identities.

Answers:

1. The sum formula for cosine is: $\cos(x + y) = \cos x \cos y - \sin x \sin y$

2. The difference formula for cosine is: $\cos(x - y) = \cos x \cos y + \sin x \sin y$

Let me know if you'd like further explanations or help with similar problems!

Related Questions:

1. How can you derive the cosine addition and subtraction formulas from the unit circle?
2. What are the corresponding sine addition and subtraction formulas?
3. How do these formulas help solve real-world problems, such as finding angles between vectors?
4. How do $\cos(x + y)$ and $\cos(x - y)$ relate to the double-angle formulas?
5. What happens to the formulas when $x = y$?

Tip: Always remember that cosine is even ($\cos(-x) = \cos x$), which plays a key role in these identities!