Question Number 217384 by MATHEMATICSAM last updated on 12/Mar/25
$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{sin351}°\:=\:−\:\sqrt{\frac{\mathrm{4}\:−\:\sqrt{\mathrm{10}\:+\:\mathrm{2}\sqrt{\mathrm{5}}}}{\mathrm{8}}\:.} \\ $$
Answered by Sutrisno last updated on 14/Mar/25
$${cos}\mathrm{18}°=\frac{\sqrt{\mathrm{10}+\mathrm{2}\sqrt{\mathrm{5}}}}{\mathrm{4}} \\ $$$${sin}\mathrm{351}°=−{sin}\mathrm{9}° \\ $$$$=−\sqrt{\frac{\mathrm{1}−{cos}\mathrm{18}°}{\mathrm{2}}} \\ $$$$=−\sqrt{\frac{\mathrm{4}−\sqrt{\mathrm{10}+\mathrm{2}\sqrt{\mathrm{5}}}}{\mathrm{8}}} \\ $$