BAMO 2009 Problem 7

Past Contests BAMO BAMO - 2009
1

Let \triangle A B C be an acute triangle with angles \alpha, \beta, and \gamma. Prove that

\frac{\cos \alpha}{\cos (\beta-\gamma)}+\frac{\cos \beta}{\cos (\gamma-\alpha)}+\frac{\cos \gamma}{\cos (\alpha-\beta)} \geq \frac{3}{2}