MathDB

2

Part of 1897 Eotvos Mathematical Competition

Problems(1)

Show that, if $\alpha$, $\beta$ and $\gamma$ are angles of an arbitrary triangle

Source: Eotvos 1897 p2

3/14/2020
Show that, if α\alpha, β\beta and γ\gamma are angles of an arbitrary triangle, sin α2 sin β2 sin γ2<14.\text{sin } \frac{\alpha}{2} \text{ sin } \frac{\beta}{2} \text{ sin } \frac{\gamma}{2} < \frac14..
inequalities