Prove that: `cos^2A+cos^2B-2cosA\ cos B cos\ (A+B)=sin^2(A+B)`

Explanation

To prove the identity \( \cos^2 A + \cos^2 B - 2 \cos A \cos B \cos(A + B) = \sin^2(A + B) \), we will follow these steps:

### Step 1: Start with the left-hand side
We begin with the left-hand side of the equation:
\[ \cos^2 A + \cos^2 B - 2 \cos A \cos B \cos(A + B) \]

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