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International Contests
Baltic Way
2014 Baltic Way
1
Trigonometric equality
Trigonometric equality
Source: Baltic Way 2014, Problem 1
November 11, 2014
trigonometry
modular arithmetic
algebra proposed
algebra
Problem Statement
Show that
cos
(
5
6
∘
)
⋅
cos
(
2
⋅
5
6
∘
)
⋅
cos
(
2
2
⋅
5
6
∘
)
⋅
.
.
.
⋅
cos
(
2
23
⋅
5
6
∘
)
=
1
2
24
.
\cos(56^{\circ}) \cdot \cos(2 \cdot 56^{\circ}) \cdot \cos(2^2\cdot 56^{\circ})\cdot . . . \cdot \cos(2^{23}\cdot 56^{\circ}) = \frac{1}{2^{24}} .
cos
(
5
6
∘
)
⋅
cos
(
2
⋅
5
6
∘
)
⋅
cos
(
2
2
⋅
5
6
∘
)
⋅
...
⋅
cos
(
2
23
⋅
5
6
∘
)
=
2
24
1
.
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