Question Number 146404 by iloveisrael last updated on 13/Jul/21
$$\:\mathrm{trigonometry} \\ $$
Commented by iloveisrael last updated on 13/Jul/21
Answered by gsk2684 last updated on 13/Jul/21
$${f}\left({x}\right)=\frac{\mathrm{1}−\mathrm{cos}\:^{\mathrm{2}} {x}+\mathrm{cos}^{\:\mathrm{4}} {x}}{\mathrm{1}−\mathrm{sin}\:^{\mathrm{2}} {x}+\mathrm{sin}\:^{\mathrm{4}} {x}} \\ $$$$=\frac{\mathrm{1}−\mathrm{cos}\:^{\mathrm{2}} {x}\left(\mathrm{1}−\mathrm{cos}^{\mathrm{2}} {x}\right)}{\mathrm{1}−\mathrm{sin}\:^{\mathrm{2}} {x}\left(\mathrm{1}−\mathrm{sin}^{\mathrm{2}} {x}\right)} \\ $$$$=\frac{\mathrm{1}−\mathrm{cos}\:^{\mathrm{2}} {x}\mathrm{sin}\:^{\mathrm{2}} {x}}{\mathrm{1}−\mathrm{sin}\:^{\mathrm{2}} {x}\mathrm{cos}\:^{\mathrm{2}} {x}}=\mathrm{1} \\ $$$${f}\left({x}\right)=\mathrm{1}\:\forall\:{x} \\ $$