Question Number 48711 by somil last updated on 27/Nov/18
Commented by mr W last updated on 27/Nov/18
$${A}+{B}+{C}=\pi \\ $$$${A}+{B}=\pi−{C} \\ $$$$\frac{{A}+{B}}{\mathrm{2}}=\frac{\pi}{\mathrm{2}}−\frac{{C}}{\mathrm{2}} \\ $$$$\mathrm{sin}\:\left(\frac{{A}+{B}}{\mathrm{2}}\right)=\mathrm{sin}\:\left(\frac{\pi}{\mathrm{2}}−\frac{{C}}{\mathrm{2}}\right)=\mathrm{cos}\:\frac{{C}}{\mathrm{2}} \\ $$
Answered by tanmay.chaudhury50@gmail.com last updated on 27/Nov/18
$${sin}\left(\frac{{A}+{B}}{\mathrm{2}}\right) \\ $$$$={sin}\left(\frac{\pi−{C}}{\mathrm{2}}\right) \\ $$$$={sin}\left(\frac{\pi}{\mathrm{2}}−\frac{{C}}{\mathrm{2}}\right) \\ $$$$={Cos}\left(\frac{{C}}{\mathrm{2}}\right) \\ $$