Q1 Matemática  (Baltic Way 2014)

Mostre que $$\cos (56^{\circ })\cdot \cos (2\cdot 56^{\circ })\cdot \cos (2^2\cdot 56^{\circ })\cdot ...\cdot \cos (2^{23}\cdot 56^{\circ })=\frac{1}{2^{24}}.$$