Here are the trigonometric formulas for the expressions $(\cos a + \cos b)$ and $(\cos a - \cos b)$:

1. Sum of cosines:

$\cos a + \cos b = 2 \cos \left(\frac{a + b}{2}\right) \cos \left(\frac{a - b}{2}\right)$

2. Difference of cosines:

$\cos a - \cos b = -2 \sin \left(\frac{a + b}{2}\right) \sin \left(\frac{a - b}{2}\right)$

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Would you like a detailed explanation or derivation of these formulas?

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5 Questions to Expand Understanding:

1. How are these formulas applied in simplifying trigonometric expressions?
2. What is the geometric interpretation of these formulas?
3. Can you derive the formulas from the sum-to-product identities?
4. What happens if $a = b$ in these formulas?
5. How do these formulas relate to solving trigonometric equations?

Tip:

To remember these formulas, note that the sum of cosines uses cosines in the expanded form, while the difference of cosines uses sines.