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Geometric inequality with sin and cos

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August 29, 2010
inequalitiestrigonometryfunctiongeometry unsolvedgeometry

Problem Statement

If TT and T1T_1 are two triangles with angles x,y,zx, y, z and x1,y1,z1x_1, y_1, z_1, respectively, prove the inequality cos⁡x1sin⁡x+cos⁡y1sin⁡y+cos⁡z1sin⁡z≤cot⁡x+cot⁡y+cot⁡z.\frac{\cos x_1}{\sin x}+\frac{\cos y_1}{\sin y}+\frac{\cos z_1}{\sin z} \leq \cot x+\cot y+\cot z.
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