MathDB
Trig equality

Source: USAMO 1992

October 27, 2005
trigonometryinductionalgebratelescoping sums

Problem Statement

Prove 1cos⁡0∘cos⁡1∘+1cos⁡1∘cos⁡2∘+⋯+1cos⁡88∘cos⁡89∘=cos⁡1∘sin⁡21∘. \frac{1}{\cos 0^\circ \cos 1^\circ} + \frac{1}{\cos 1^\circ \cos 2^\circ} + \cdots + \frac{1}{\cos 88^\circ \cos 89^\circ} = \frac{\cos 1^\circ}{\sin^2 1^\circ}.
Back to ProblemsView on AoPS