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Prove that : (cos alpha + cos beta)^2 + ...

Prove that : `(cos alpha + cos beta)^2 + (sin alpha + sin beta)^2 = 4 cos^2 ((alpha-beta)/(2))`

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To prove the identity \((\cos \alpha + \cos \beta)^2 + (\sin \alpha + \sin \beta)^2 = 4 \cos^2\left(\frac{\alpha - \beta}{2}\right)\), we will start with the left-hand side (LHS) and simplify it step by step. ### Step 1: Expand the LHS We start with the left-hand side: \[ (\cos \alpha + \cos \beta)^2 + (\sin \alpha + \sin \beta)^2 \] Using the formula \((a + b)^2 = a^2 + 2ab + b^2\), we can expand both terms: ...
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