Question Number 86614 by mathocean1 last updated on 29/Mar/20
$${ABC}\:{is}\:{an}\:{isocel}\:{triangle}\:{such}\:{as} \\ $$$${AB}={AC}=\mathrm{3}\:\:{and}\:{BC}=\mathrm{4} \\ $$$$\alpha\:,\:\beta\:,\:{and}\:\gamma\:{are}\:{its}\:{angles}. \\ $$$${Show}\:{that}\:{cos}\left(\frac{\alpha+\beta}{\mathrm{2}}\right)={sin}\left(\frac{\gamma}{\mathrm{2}}\right) \\ $$$${Hi}\:{sirs}… \\ $$
Answered by TANMAY PANACEA. last updated on 29/Mar/20
$$\frac{\alpha+\beta}{\mathrm{2}} \\ $$$$=\frac{\pi−\gamma}{\mathrm{2}} \\ $$$$=\frac{\pi}{\mathrm{2}}−\frac{\gamma}{\mathrm{2}} \\ $$$${cos}\left(\frac{\alpha+\beta}{\mathrm{2}}\right) \\ $$$$={cos}\left(\frac{\pi}{\mathrm{2}}−\frac{\gamma}{\mathrm{2}}\right) \\ $$$$={sin}\frac{\gamma}{\mathrm{2}} \\ $$$$ \\ $$
Commented by mathocean1 last updated on 29/Mar/20
$${thank}\:{you}\:{sir}. \\ $$