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

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