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Poland Contests
Poland - Second Round
1964 Poland - Second Round
1
sum 1/sin 2na = ...
sum 1/sin 2na = ...
Source: Polish MO Second Round 1964 p1
August 31, 2024
trigonometry
algebra
Problem Statement
Prove that if
n
n
n
is a natural number and the angle
α
\alpha
α
is not a multiple of
18
0
∘
2
n
\frac{180^{\circ}}{2^n}
2
n
18
0
∘
, then
1
sin
2
α
+
1
sin
4
α
+
1
sin
8
α
+
.
.
.
+
=
c
t
g
α
−
c
t
g
2
n
α
.
\frac{1}{\sin 2\alpha} + \frac{1}{\sin 4\alpha} + \frac{1}{\sin 8\alpha} + ... + = ctg \alpha - ctg 2^n \alpha.
sin
2
α
1
+
sin
4
α
1
+
sin
8
α
1
+
...
+
=
c
t
gα
−
c
t
g
2
n
α
.
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