Question Number 31745 by pieroo last updated on 13/Mar/18
$$\mathrm{pls},\:\mathrm{why}\:\mathrm{is}\:\mathrm{cos}^{\mathrm{4}} −\mathrm{sin}^{\mathrm{4}\:} \:=\:\mathrm{cos}^{\mathrm{2}} −\mathrm{sin}^{\mathrm{2}} ? \\ $$
Answered by Tinkutara last updated on 13/Mar/18
$$\mathrm{cos}^{\mathrm{4}} \:\theta−\mathrm{sin}^{\mathrm{4}} \:\theta \\ $$$$=\left(\mathrm{cos}^{\mathrm{2}} \:\theta−\mathrm{sin}^{\mathrm{2}} \:\theta\right)\left(\mathrm{cos}^{\mathrm{2}} \:\theta+\mathrm{sin}^{\mathrm{2}} \:\theta\right) \\ $$$$=\left(\mathrm{cos}^{\mathrm{2}} \:\theta−\mathrm{sin}^{\mathrm{2}} \:\theta\right)\left(\mathrm{1}\right) \\ $$$$=\mathrm{cos}^{\mathrm{2}} \:\theta−\mathrm{sin}^{\mathrm{2}} \:\theta \\ $$