Question Number 219839 by Lekhraj last updated on 02/May/25
Answered by golsendro last updated on 03/May/25
$$\:\mathrm{sin}\:\mathrm{2}\theta\:=\:\mathrm{2}\left(\frac{\sqrt{\mathrm{4}−\sqrt{\mathrm{5}}}\:+\sqrt{\sqrt{\mathrm{5}}−\mathrm{2}}}{\mathrm{2}}\:\right)\left(\frac{\sqrt{\mathrm{4}−\sqrt{\mathrm{5}}}−\sqrt{\sqrt{\mathrm{5}}−\mathrm{2}}}{\mathrm{2}}\:\right) \\ $$$$\:=\:\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{4}−\sqrt{\mathrm{5}}\:−\sqrt{\mathrm{5}}\:+\mathrm{2}\:\right) \\ $$$$\:=\:\mathrm{3}−\sqrt{\mathrm{5}}\: \\ $$