Question Number 108628 by I want to learn more last updated on 18/Aug/20
$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{inequality}\:\:\mid\mathrm{cos}\:\mathrm{x}\mid\:\:\geqslant\:\:\:\mathrm{1}\:\:−\:\:\mathrm{sin}^{\mathrm{2}} \mathrm{x}\:\:\:\:\mathrm{hold}\:\mathrm{true}\:\mathrm{for}\:\mathrm{all}\:\:\mathrm{x}\:\in\:\mathbb{R} \\ $$
Commented by mr W last updated on 18/Aug/20
$$\mid\mathrm{cos}\:{x}\mid\leqslant\mathrm{1} \\ $$$$\Rightarrow\mid\mathrm{cos}\:{x}\mid\geqslant\mathrm{cos}^{\mathrm{2}} \:{x}=\mathrm{1}−\mathrm{sin}^{\mathrm{2}} \:{x} \\ $$
Commented by I want to learn more last updated on 18/Aug/20
$$\mathrm{Thanks}\:\mathrm{sir},\:\mathrm{i}\:\mathrm{appreciate}. \\ $$
Commented by I want to learn more last updated on 18/Aug/20
$$\mathrm{please}\:\mathrm{sir}\:\mathrm{help}\:\mathrm{with}\:\:\:\mathrm{Q}\:\mathrm{108626} \\ $$
Commented by Aziztisffola last updated on 18/Aug/20
$$\mathrm{look}\:\mathrm{at}\:\mathrm{the}\:\mathrm{answer}\:\mathrm{to}\:\mathrm{get}\:\mathrm{an}\:\mathrm{idea}. \\ $$