Question Number 172787 by mnjuly1970 last updated on 01/Jul/22
$$ \\ $$$$\:\:\:\mathrm{In}\:\:\mathrm{A}\overset{\Delta} {\mathrm{B}C}\:\:,\:\mathrm{prove}\:\:\mathrm{that}\: \\ $$$$\:{sin}\left(\frac{\mathrm{A}}{\mathrm{2}}\right).{sin}\left(\frac{\mathrm{B}}{\mathrm{2}}\right).{sin}\left(\frac{\mathrm{C}}{\mathrm{2}}\right)\:\leqslant\:\frac{\mathrm{1}}{\mathrm{8}} \\ $$$$\:\:\:−−−−−−−− \\ $$$$ \\ $$