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If
S
=
cos
2
π
n
+
cos
2
2
π
n
+
⋯
+
cos
2
(
n
−
1
)
π
n
S = \cos^2 \frac{\pi}{n} + \cos^2 \frac{2\pi}{n} + \dots + \cos^2 \frac{(n-1)\pi}{n}
S
=
cos
2
n
π
+
cos
2
n
2
π
+
⋯
+
cos
2
n
(
n
−
1
)
π
…
Problem
If
S
=
cos
2
π
n
+
cos
2
2
π
n
+
⋯
+
cos
2
(
n
−
1
)
π
n
S = \cos^2 \frac{\pi}{n} + \cos^2 \frac{2\pi}{n} + \dots + \cos^2 \frac{(n-1)\pi}{n}
S
=
cos
2
n
π
+
cos
2
n
2
π
+
⋯
+
cos
2
n
(
n
−
1
)
π
, then S equals a.
n
2
(
n
+
1
)
\frac{n}{2(n+1)}
2
(
n
+
1
)
n
b.
1
2
(
n
−
1
)
\frac{1}{2(n-1)}
2
(
n
−
1
)
1
c.
1
2
(
n
−
2
)
\frac{1}{2(n-2)}
2
(
n
−
2
)
1
d.
n
2
\frac{n}{2}
2
n
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