MathDB

451

Part of 1987 All Soviet Union Mathematical Olympiad

Problems(1)

ASU 451 All Soviet Union MO 1987 cos a, cos 2a, cos 4a, ... , cos((2^n)a)<0

Source:

8/7/2019
Prove such aa, that all the numbers cos⁡a,cos⁡2a,cos⁡4a,...,cos⁡(2na)\cos a, \cos 2a, \cos 4a, ... , \cos (2^na) are negative.
trigonometryalgebra