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Prove that cos(pi/11) + cos(3pi/11) + cos(5pi/11) + cos(7pi/11) + cos(9pi/11) = 1/2.

1. Proof: multiply the sum by 2 sin(pi/11) and telescope to get sin(10pi/11)/(2 sin(pi/11)) = 1/2
2. The sum equals 1
3. The sum equals 0
4. The sum equals -1/2

Correct answer: Proof: multiply the sum by 2 sin(pi/11) and telescope to get sin(10pi/11)/(2 sin(pi/11)) = 1/2

Solution

Multiplying by 2 sin(pi/11) telescopes the products to sin(10pi/11), and since sin(10pi/11) = sin(pi/11), the sum equals 1/2.

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