Question Number 78643 by thiruppathit883@gmail.com last updated on 19/Jan/20
$$\mathrm{sin}\:\mathrm{20}×\mathrm{sin}\:\mathrm{40}×\mathrm{sin}\:\mathrm{80}=\sqrt{\mathrm{3}/\mathrm{8}} \\ $$
Commented by jagoll last updated on 19/Jan/20
$$\mathrm{using}\:\mathrm{formula} \\ $$$$\mathrm{sin}\:\theta×\mathrm{sin}\:\left(\mathrm{60}^{\mathrm{o}} −\theta\right)×\mathrm{sin}\:\left(\mathrm{60}^{\mathrm{o}} +\theta\right)= \\ $$$$\frac{\mathrm{1}}{\mathrm{4}}\mathrm{sin}\:\mathrm{3}\theta\: \\ $$
Commented by jagoll last updated on 19/Jan/20
$$\mathrm{put}\:\theta\:=\:\mathrm{20}^{\mathrm{o}} \:,\:\mathrm{sin}\:\mathrm{20}^{\mathrm{o}} ×\mathrm{sin}\:\mathrm{40}^{\mathrm{o}} ×\mathrm{sin}\:\mathrm{80}^{\mathrm{o}} = \\ $$$$\frac{\mathrm{1}}{\mathrm{4}}\mathrm{sin}\:\mathrm{60}^{\mathrm{o}} \:=\:\frac{\mathrm{1}}{\mathrm{8}}\sqrt{\mathrm{3}} \\ $$