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Bulgaria Contests
Bulgaria National Olympiad
1972 Bulgaria National Olympiad
Problem 3
Problem 3
Part of
1972 Bulgaria National Olympiad
Problems
(1)
trigonometric equality
Source: Bulgaria 1972 P3
6/21/2021
Prove the equality:
∑
k
=
1
n
−
1
1
sin
2
(
2
k
+
1
)
π
2
n
=
n
2
\sum_{k=1}^{n-1}\frac1{\sin^2\frac{(2k+1)\pi}{2n}}=n^2
k
=
1
∑
n
−
1
sin
2
2
n
(
2
k
+
1
)
π
1
=
n
2
where
n
n
n
is a natural number.H. Lesov
trigonometry
algebra