Problem #PRU-110153

Problems Calculus Real numbers Integer and fractional parts. Archimedean property Methods Pigeonhole principle Pigeonhole principle (angles and lengths)
 13–15  3.0

Problem

The sum of the positive numbers a,b,c is π/2. Prove that cos⁡a+cos⁡b+cos⁡c>sin⁡a+sin⁡b+sin⁡c.