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cos20-cos40-cos80-




Question Number 103299 by B. H 28 last updated on 14/Jul/20
cos20°cos40°cos80°=...?
$${cos}\mathrm{20}°{cos}\mathrm{40}°{cos}\mathrm{80}°=…? \\ $$
Answered by bemath last updated on 14/Jul/20
(1/4) cos 3θ = (1/4)×cos 3.20^o =(1/4)×(1/2) = (1/8)
$$\frac{\mathrm{1}}{\mathrm{4}}\:\mathrm{cos}\:\mathrm{3}\theta\:=\:\frac{\mathrm{1}}{\mathrm{4}}×\mathrm{cos}\:\mathrm{3}.\mathrm{20}^{{o}} =\frac{\mathrm{1}}{\mathrm{4}}×\frac{\mathrm{1}}{\mathrm{2}}\:=\:\frac{\mathrm{1}}{\mathrm{8}} \\ $$
Answered by Dwaipayan Shikari last updated on 14/Jul/20
(1/(2sin20°))(sin40°cos40°cos80°)=(1/(4sin20°))(sin80°cos80°)=((sin160°)/(8sin20°))=(1/8)
$$\frac{\mathrm{1}}{\mathrm{2}{sin}\mathrm{20}°}\left({sin}\mathrm{40}°{cos}\mathrm{40}°{cos}\mathrm{80}°\right)=\frac{\mathrm{1}}{\mathrm{4}{sin}\mathrm{20}°}\left({sin}\mathrm{80}°{cos}\mathrm{80}°\right)=\frac{{sin}\mathrm{160}°}{\mathrm{8}{sin}\mathrm{20}°}=\frac{\mathrm{1}}{\mathrm{8}} \\ $$

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