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Find the sum of the series sin(pi/n) + sin(3pi/n) + sin(5pi/n) +... up to n terms.

1. cot(pi/(2n))
2. tan(pi/(2n))
3. 1
4. n/2

Correct answer: cot(pi/(2n))

Solution

Applying the AP sine-sum formula with a = pi/n, d = 2pi/n gives sin(pi)/sin(pi/n) * sin(...) form; after simplification the sum equals cot(pi/(2n)).

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