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Inequality involving Sine values

Source: Germany 2011, Grade 13 - #1

May 30, 2016
inequalitiestrigonometryalgebra unsolvedalgebrasine double angle

Problem Statement

Prove for each non-negative integer nn and real number xx the inequality sin⁡x⋅(nsin⁡x−sin⁡nx)≥0 \sin{x} \cdot(n \sin{x}-\sin{nx}) \geq 0
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