Convert the products into sum or difference. If angles are given in degrees, evaluate from tables.
`2 cos 5 theta cos 3 theta `

Answer

To convert the product \(2 \cos(5\theta) \cos(3\theta)\) into a sum or difference, we can use the trigonometric identity:

\[ 2 \cos A \cos B = \cos(A + B) + \cos(A - B) \]

### Step-by-Step Solution:

1. **Identify \(A\) and \(B\)**:
- Here, let \(A = 5\theta\) and \(B = 3\theta\).

2. **Apply the identity**:
- According to the identity, we can rewrite \(2 \cos(5\theta) \cos(3\theta)\) as:
\[ 2 \cos(5\theta) \cos(3\theta) = \cos(5\theta + 3\theta) + \cos(5\theta - 3\theta) \]

3. **Simplify the angles**:
- Now calculate \(A + B\) and \(A - B\):
\[ A + B = 5\theta + 3\theta = 8\theta \]
\[ A - B = 5\theta - 3\theta = 2\theta \]

4. **Write the final expression**:
- Substitute back into the equation:
\[ 2 \cos(5\theta) \cos(3\theta) = \cos(8\theta) + \cos(2\theta) \]

### Final Answer:
\[ 2 \cos(5\theta) \cos(3\theta) = \cos(8\theta) + \cos(2\theta) \]