MathDB
Tangent inequality

Source: Austrian-Polish 1978, Problem 3

July 5, 2015
trigonometryinequalities

Problem Statement

Prove that tan⁡1∘⋅tan⁡2∘⋅⋯⋅tan⁡44∘44<2−1<tan⁡1∘+tan⁡2∘+⋯+tan⁡44∘44.\sqrt[44]{\tan 1^\circ\cdot \tan 2^\circ\cdot \dots\cdot \tan 44^\circ}<\sqrt 2-1<\frac{\tan 1^\circ+ \tan 2^\circ+\dots+\tan 44^\circ}{44}.
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