Trigonometry (2)

Geometry Level 4

Sn=cos2πn+cos22πn+cos23πn++cos2(n1)πn\large S_n= \cos^2 \dfrac{π}{n} + \cos^2 \dfrac{2π}{n} + \cos^2 \dfrac{3π}{n} + \cdots + \cos^2 \dfrac{(n-1)π}{n}

For integer n2n\geq 2, simplify SnS_n to an algebraic function of nn.

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