Trigonometry crush 2

Geometry Level 2

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

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

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