Prove that: `(cosx+cosy)^2+(sinx-siny)^2``=4cos^2``(x+y)/2`

Explanation

To prove the identity \((\cos x + \cos y)^2 + (\sin x - \sin y)^2 = 4 \cos^2\left(\frac{x + y}{2}\right)\), we will follow these steps:

### Step 1: Expand the left-hand side
We start with the left-hand side:
\[ (\cos x + \cos y)^2 + (\sin x - \sin y)^2 \]
Using the algebraic identities:
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