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Evaluate (cos(alpha) + cos(beta))² + (sin(alpha) + sin(beta))².

1. 4*cos²((alpha - beta)/2)
2. 2*cos²((alpha - beta)/2)
3. 4*sin²((alpha - beta)/2)
4. 2 + 2*cos(alpha + beta)

Correct answer: 4*cos²((alpha - beta)/2)

Solution

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

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