Question Number 145852 by mathdanisur last updated on 08/Jul/21
$${sin}\frac{\pi}{\mathrm{24}}\centerdot{cos}\frac{\pi}{\mathrm{24}}\centerdot{cos}\frac{\pi}{\mathrm{12}}=? \\ $$
Answered by waiphyoemaung last updated on 08/Jul/21
$$\mathrm{solution} \\ $$$$\mathrm{sin}\frac{\pi}{\mathrm{24}}.\mathrm{cos}\frac{\pi}{\mathrm{24}}.\mathrm{cos}\frac{\pi}{\mathrm{12}} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}.\left(\mathrm{2sin}\frac{\pi}{\mathrm{24}}\mathrm{cos}\frac{\pi}{\mathrm{24}}\right)\mathrm{cos}\frac{\pi}{\mathrm{12}} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}.\mathrm{sin}\frac{\pi}{\mathrm{12}}.\mathrm{cos}\frac{\pi}{\mathrm{12}}\:\:\left(\because\mathrm{sin}\:\mathrm{2}\alpha=\mathrm{2sin}\:\alpha\:\mathrm{cos}\:\alpha\right) \\ $$$$=\frac{\mathrm{1}}{\mathrm{4}}.\mathrm{2sin}\frac{\pi}{\mathrm{12}}.\mathrm{cos}\frac{\pi}{\mathrm{12}} \\ $$$$=\frac{\mathrm{1}}{\mathrm{4}}.\mathrm{sin}\frac{\pi}{\mathrm{6}} \\ $$$$=\frac{\mathrm{1}}{\mathrm{4}}×\frac{\mathrm{1}}{\mathrm{2}}\:\:\:\left(\because\mathrm{sin}\frac{\pi}{\mathrm{6}}=\frac{\mathrm{1}}{\mathrm{2}}\right) \\ $$$$=\frac{\mathrm{1}}{\mathrm{8}} \\ $$
Commented by mathdanisur last updated on 08/Jul/21
$${Thanks}\:{Ser}\:{cool} \\ $$