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

Source: Eotvos 1897 p2

March 14, 2020
inequalities

Problem Statement

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..
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