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Prove that (cos α + cos β)^2 + (sin α - sin β)^2 = 4 cos^2(α + β)/2

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Prove that (cos α + cos β)2 + (sin α - sin β)2 = 4 cos2(α + β)/2

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LHS = (cos α + cos β)2 + (sin α - sin β)2

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