Question Number 176140 by mnjuly1970 last updated on 13/Sep/22
$$ \\ $$$$\:\:\:{in}\:{A}\overset{\Delta} {{B}C}\:,\:{prove}\:{that}: \\ $$$$\:\:{sin}\left(\mathrm{2}{A}\right)+{sin}\left(\mathrm{2}{B}\right)+{sin}\left(\mathrm{2}{C}\right)\: \\ $$$$\leqslant{cos}\:\left(\frac{{A}}{\mathrm{2}}\right)\:+\:{cos}\:\left(\frac{{B}}{\mathrm{2}}\right)+{cos}\left(\frac{{C}}{\mathrm{2}}\right) \\ $$$$ \\ $$