Prove that:
`(cosA+cosB)^(2)+(sinA+sinB)^(2)=4cos^(2)(A-B)/2`

Explanation

To prove that \((\cos A + \cos B)^2 + (\sin A + \sin B)^2 = 4 \cos^2\left(\frac{A - B}{2}\right)\), we will follow these steps:

### Step 1: Expand the left-hand side
We start with the expression \((\cos A + \cos B)^2 + (\sin A + \sin B)^2\).

Using the identity \((x + y)^2 = x^2 + y^2 + 2xy\), we can expand both terms:

\[
...