MathDB

78

Part of 1986 IMO Longlists

Problems(1)

Geometric inequality with sin and cos

Source:

8/29/2010
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.
inequalitiestrigonometryfunctiongeometry unsolvedgeometry