\[ \large ( \cos\alpha + \cos\beta)^2 + (\sin\alpha + \sin\beta)^2 = p \cdot \cos^2 \left( \frac{\alpha - \beta}2\right) \]

Above shows a trigonometric identity for all \(\alpha\) and \(\beta\) with constant \(p\). Find the value of \(p\).

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