New Infinite Products of Cosines and Viète-Like Formulae

Abstract

SummaryIn this article, the authors show that Viète's formula is only the tip of the iceberg. Under the surface, they search for curious and interesting Viète-like infinite products, rare species made of products of nested square roots of 2, but here with some minus signs occurring inside. To explore this fascinating world, they only use the simple trigonometric identity cos x = 2 cos((π + 2x)/4) cos ((π - 2x)/4), combined with a recent formula by L. D. Servi.