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Question Number 148388 by mathdanisur last updated on 27/Jul/21

cos40°(1 - 2cos80°) = ?

$${cos}\mathrm{40}°\left(\mathrm{1}\:-\:\mathrm{2}{cos}\mathrm{80}°\right)\:=\:? \\ $$

Answered by liberty last updated on 27/Jul/21

cos 40°(1−2(2cos^2 40°−1))  = cos 40°(3−4cos^2 40°)  =3cos 40°−4cos^3 40°  =−cos 120°=(1/2)

$$\mathrm{cos}\:\mathrm{40}°\left(\mathrm{1}−\mathrm{2}\left(\mathrm{2cos}\:^{\mathrm{2}} \mathrm{40}°−\mathrm{1}\right)\right) \\ $$$$=\:\mathrm{cos}\:\mathrm{40}°\left(\mathrm{3}−\mathrm{4cos}\:^{\mathrm{2}} \mathrm{40}°\right) \\ $$$$=\mathrm{3cos}\:\mathrm{40}°−\mathrm{4cos}\:^{\mathrm{3}} \mathrm{40}° \\ $$$$=−\mathrm{cos}\:\mathrm{120}°=\frac{\mathrm{1}}{\mathrm{2}} \\ $$

Commented by mathdanisur last updated on 27/Jul/21

Thanks Ser

$${Thanks}\:{Ser} \\ $$

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