# Verify the identity secx-secx sin^2x= cosx

Verify the identity $\mathrm{sec}x-\mathrm{sec}x{\mathrm{sin}}^{2}x=\mathrm{cos}x$
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Alix Ortiz
$\mathrm{sec}x-\mathrm{sec}x{\mathrm{sin}}^{2}x=\mathrm{cos}x$
$\mathrm{sec}x\left(1-{\mathrm{sin}}^{2}x\right)=\mathrm{cos}x$
because ${\mathrm{sin}}^{x}+{\mathrm{cos}}^{x}=1,1-{\mathrm{sin}}^{2}x={\mathrm{cos}}^{2}x$
$\mathrm{sec}x{\mathrm{cos}}^{2}x=\mathrm{cos}x$
$\left(\frac{I}{\mathrm{cos}x}\right){\mathrm{cos}}^{2}x=\mathrm{cos}x$
$\mathrm{cos}x=\mathrm{cos}x$