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Solve-1-cos-70-2-cos-10-




Question Number 106493 by mohammad17 last updated on 05/Aug/20
Solve?  (1)cos(70)  (2)cos(10)
$${Solve}? \\ $$$$\left(\mathrm{1}\right){cos}\left(\mathrm{70}\right) \\ $$$$\left(\mathrm{2}\right){cos}\left(\mathrm{10}\right) \\ $$
Commented by malwaan last updated on 05/Aug/20
cos 10 = cos 70 + cos 50
$${cos}\:\mathrm{10}\:=\:{cos}\:\mathrm{70}\:+\:{cos}\:\mathrm{50} \\ $$
Answered by bemath last updated on 05/Aug/20
consider cos 3x=4cos^3 x−3cos x  put x=10°  cos 30°=4cos^3  10°−3cos 10°  ((√3)/2) = 4cos^3 10°−3cos 10°  solve via Cardano method
$$\mathrm{consider}\:\mathrm{cos}\:\mathrm{3x}=\mathrm{4cos}\:^{\mathrm{3}} \mathrm{x}−\mathrm{3cos}\:\mathrm{x} \\ $$$$\mathrm{put}\:\mathrm{x}=\mathrm{10}° \\ $$$$\mathrm{cos}\:\mathrm{30}°=\mathrm{4cos}^{\mathrm{3}} \:\mathrm{10}°−\mathrm{3cos}\:\mathrm{10}° \\ $$$$\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\:=\:\mathrm{4cos}\:^{\mathrm{3}} \mathrm{10}°−\mathrm{3cos}\:\mathrm{10}° \\ $$$$\mathrm{solve}\:\mathrm{via}\:\mathrm{Cardano}\:\mathrm{method} \\ $$
Commented by mohammad17 last updated on 05/Aug/20
sir can you give be raw the Cardano method
$${sir}\:{can}\:{you}\:{give}\:{be}\:{raw}\:{the}\:{Cardano}\:{method} \\ $$
Commented by malwaan last updated on 06/Aug/20
I solved it by trigonomitric  method and get the solutions  cos 10 ; −cos 70 ; −cos 50
$${I}\:{solved}\:{it}\:{by}\:{trigonomitric} \\ $$$${method}\:{and}\:{get}\:{the}\:{solutions} \\ $$$${cos}\:\mathrm{10}\:;\:−{cos}\:\mathrm{70}\:;\:−{cos}\:\mathrm{50} \\ $$

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