Question Number 87624 by john santu last updated on 05/Apr/20
$$\mathrm{find}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{cos}\:^{\mathrm{2}} \mathrm{w}\:+ \\ $$$$\mathrm{sec}\:^{\mathrm{2}} \mathrm{w}\: \\ $$
Commented by john santu last updated on 05/Apr/20
$$\mathrm{AM}\:\geqslant\:\mathrm{GM} \\ $$$$\frac{\mathrm{cos}\:^{\mathrm{2}} \:\mathrm{w}+\mathrm{sec}\:^{\mathrm{2}} \:\mathrm{w}}{\mathrm{2}}\:\geqslant\:\sqrt{\mathrm{cos}\:^{\mathrm{2}} \mathrm{w}×\mathrm{sec}\:^{\mathrm{2}} \mathrm{w}} \\ $$$$\mathrm{cos}\:^{\mathrm{2}} \mathrm{w}\:\:+\:\mathrm{sec}\:^{\mathrm{2}} \mathrm{w}\:\geqslant\:\mathrm{2} \\ $$$$\mathrm{minimum}\:\mathrm{value}\:=\:\mathrm{2} \\ $$