MathDB

11.5

Part of 1995 All-Russian Olympiad Regional Round

Problems(1)

cosA+cosB+cosC<=\sqrt5 All-Russian MO 1995 Regional (R4) 11.5

Source:

8/26/2024
Angles α,β,γ\alpha, \beta, \gamma satisfy the inequality sin⁡α+sin⁡β+sin⁡γ≥2\sin \alpha +\sin \beta +\sin \gamma \ge 2. Prove that cos⁡α+cos⁡β+cos⁡γ≤5.\cos \alpha + \cos \beta +\cos \gamma \le \sqrt5.
algebrainequalitiestrigonometry