19

Part of 1991 IMO Shortlist

Problems(1)

Source:

\alpha

be a rational number with

0 < \alpha < 1

and \cos (3 \pi \alpha) \plus{} 2\cos(2 \pi \alpha) \equal{} 0. Prove that \alpha \equal{} \frac {2}{3}.

trigonometryrational numbersIMO Shortlist