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Evaluate whether the following is a valid identity: 2*cos(pi/13)*cos(9pi/13) + cos(3pi/13)*cos(5pi/13) = 0.

1. True
2. False
3. Cannot be determined
4. None of these

Correct answer: True

Solution

Expanding both products into sums and using cos(pi - x) = -cos x causes all terms to cancel, giving 0.

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