MathDB

tg \frac{a + b}{2} \leq \frac{tg a+ tg b}{2

Source: Polish MO second round 1959 p3

August 29, 2024

trigonometryinequalities

Problem Statement

Prove that if

0 \leq \alpha < \frac{\pi}{2}

and

0 \leq \beta < \frac{\pi}{2}

, then

tg \frac{\alpha + \beta}{2} \leq \frac{tg \alpha + tg \beta}{2}.