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MathNet 2014 Question 84

Math Olympiad Vault · MathNet 2014

Question 84

Show that
$$
\cos(56^\circ) \cdot \cos(2 \cdot 56^\circ) \cdot \dots \cdot \cos(2^{23} \cdot 56^\circ) = \frac{1}{2^{23}}
$$