Question Number 148388 by mathdanisur last updated on 27/Jul/21
$${cos}\mathrm{40}°\left(\mathrm{1}\:-\:\mathrm{2}{cos}\mathrm{80}°\right)\:=\:? \\ $$
Answered by liberty last updated on 27/Jul/21
$$\mathrm{cos}\:\mathrm{40}°\left(\mathrm{1}−\mathrm{2}\left(\mathrm{2cos}\:^{\mathrm{2}} \mathrm{40}°−\mathrm{1}\right)\right) \\ $$$$=\:\mathrm{cos}\:\mathrm{40}°\left(\mathrm{3}−\mathrm{4cos}\:^{\mathrm{2}} \mathrm{40}°\right) \\ $$$$=\mathrm{3cos}\:\mathrm{40}°−\mathrm{4cos}\:^{\mathrm{3}} \mathrm{40}° \\ $$$$=−\mathrm{cos}\:\mathrm{120}°=\frac{\mathrm{1}}{\mathrm{2}} \\ $$
Commented by mathdanisur last updated on 27/Jul/21
$${Thanks}\:{Ser} \\ $$