Trigonometry crush 2

Geometry Level 3

(cosα+cosβ)2+(sinα+sinβ)2=pcos2(αβ2) \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 α\alpha and β\beta with constant pp. Find the value of pp.

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