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Let S = cos²(pi/n) + cos²(2*pi/n) +... + cos²((n-1)*pi/n), where n is a natural number with n >= 2. Find S.

1. (n - 2) / 2
2. n / (2*(n + 1))
3. 1 / (2*(n - 1))
4. n / 2

Correct answer: (n - 2) / 2

Solution

Writing each term as (1 + cos(2k*pi/n))/2, the constant part gives (n-1)/2 and the cosine sum gives -1/2, totaling (n-2)/2.

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