Question Number 139409 by henderson last updated on 26/Apr/21
$$\mathrm{hi}\:! \\ $$$$\mathrm{prove}\:\mathrm{this}\::\: \\ $$$${cos}\:\frac{\pi}{\mathrm{10}}\:+\:{cos}\:\frac{\mathrm{4}\pi}{\mathrm{10}}\:+\:{cos}\:\frac{\mathrm{6}\pi}{\mathrm{10}}\:+\:{cos}\:\frac{\mathrm{9}\pi}{\mathrm{10}}\:=\:\mathrm{0}. \\ $$$$\left(\mathrm{by}\:\mathrm{the}\:\mathrm{easiest}\:\mathrm{possible}\:\mathrm{way}…!\right) \\ $$
Answered by mr W last updated on 26/Apr/21
$$\mathrm{cos}\:\alpha+\mathrm{cos}\:\left(\pi−\alpha\right)=\mathrm{0} \\ $$$$\mathrm{cos}\:\frac{\pi}{\mathrm{10}}+\mathrm{cos}\:\frac{\mathrm{9}\pi}{\mathrm{10}}=\mathrm{0} \\ $$$$\mathrm{cos}\:\frac{\mathrm{4}\pi}{\mathrm{10}}+\mathrm{cos}\:\frac{\mathrm{6}\pi}{\mathrm{10}}=\mathrm{0} \\ $$$$….=\mathrm{0} \\ $$
Commented by henderson last updated on 26/Apr/21
$$\mathrm{waoh}\:!\:\mathrm{thank}\:\mathrm{u}\:\mathrm{very}\:\mathrm{much},\:\mathrm{sir}\:\mathrm{w}\:! \\ $$