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