The sum of positive numbers $a, b, c$ is equal to $\pi/2$. Prove that $$\cos a + \cos b + \cos c > \sin a + \sin b + \sin c.$$
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Tags: trigonometry, algebra, inequalities
The sum of positive numbers $a, b, c$ is equal to $\pi/2$. Prove that $$\cos a + \cos b + \cos c > \sin a + \sin b + \sin c.$$