Convert the sums or differences into products:
`cos 79^(@) + cos 11 ^(@)`

Answer

To convert the sum \( \cos 79^\circ + \cos 11^\circ \) into a product, we can use the formula for the sum of cosines:

\[ \cos A + \cos B = 2 \cos\left(\frac{A + B}{2}\right) \cos\left(\frac{A - B}{2}\right) \]

### Step-by-Step Solution:

1. **Identify \( A \) and \( B \)**:
- Let \( A = 79^\circ \) and \( B = 11^\circ \).

2. **Calculate \( A + B \)**:
- \( A + B = 79^\circ + 11^\circ = 90^\circ \).

3. **Calculate \( A - B \)**:
- \( A - B = 79^\circ - 11^\circ = 68^\circ \).

4. **Apply the formula**:
- Substitute \( A + B \) and \( A - B \) into the formula:
\[ \cos 79^\circ + \cos 11^\circ = 2 \cos\left(\frac{90^\circ}{2}\right) \cos\left(\frac{68^\circ}{2}\right) \]

5. **Simplify the angles**:
- \( \frac{90^\circ}{2} = 45^\circ \)
- \( \frac{68^\circ}{2} = 34^\circ \)

6. **Final expression**:
- Therefore, we have:
\[ \cos 79^\circ + \cos 11^\circ = 2 \cos(45^\circ) \cos(34^\circ) \]

### Final Answer:
\[ \cos 79^\circ + \cos 11^\circ = 2 \cos(45^\circ) \cos(34^\circ) \]

---