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Prove that (cos(alpha) + cos(beta))² + (sin(alpha) - sin(beta))² = 4 cos²((alpha + beta)/2).

1. Identity is true (proved)
2. Identity is false
3. RHS should be 4 sin²((alpha+beta)/2)
4. RHS should be 2 cos²((alpha+beta)/2)

Correct answer: Identity is true (proved)

Solution

Expanding gives 2 + 2 cos(alpha+beta) = 2(1 + cos(alpha+beta)) = 4 cos²((alpha+beta)/2).

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