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Russian trig inequality

Source: Russian MO 1994

June 30, 2017
InequalitytrigonometryTrigonometric inequalityinequalities

Problem Statement

Prove that for all x∈(0,π3)x \in \left( 0, \frac{\pi}{3} \right) inequality sin2x+cosx>1sin2x+cosx>1 holds.
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