MathDB

1

Part of 2014 Baltic Way

Problems(1)

Trigonometric equality

Source: Baltic Way 2014, Problem 1

11/11/2014
Show that cos⁡(56∘)⋅cos⁡(2⋅56∘)⋅cos⁡(22⋅56∘)⋅...⋅cos⁡(223⋅56∘)=1224.\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}} .
trigonometrymodular arithmeticalgebra proposedalgebra