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Question Number 176140 by mnjuly1970 last updated on 13/Sep/22

     in AB^Δ C , prove that:    sin(2A)+sin(2B)+sin(2C)   ≤cos ((A/2)) + cos ((B/2))+cos((C/2))

$$ \\ $$$$\:\:\:{in}\:{A}\overset{\Delta} {{B}C}\:,\:{prove}\:{that}: \\ $$$$\:\:{sin}\left(\mathrm{2}{A}\right)+{sin}\left(\mathrm{2}{B}\right)+{sin}\left(\mathrm{2}{C}\right)\: \\ $$$$\leqslant{cos}\:\left(\frac{{A}}{\mathrm{2}}\right)\:+\:{cos}\:\left(\frac{{B}}{\mathrm{2}}\right)+{cos}\left(\frac{{C}}{\mathrm{2}}\right) \\ $$$$ \\ $$

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