MathDB

6

Part of 1965 German National Olympiad

Problems(1)

cos \alpha + \cos\beta + \cos\beta <= \frac{3}{2}

Source: Germany 1965 p6

2/21/2020
Let α,β,γ\alpha,\beta, \gamma be the angles of a triangle. Prove that cos⁡α,+cos⁡β+cos⁡γ≤32\cos\alpha, + \cos\beta + \cos\gamma \le \frac{3}{2} and find the cases of equality.
trigonometryinequalitiesGeometric Inequalitiesgeometry