# Solve the equationsec x - sec x sin^{2}x = cos x

Solve the equation

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Talisha
Work with a left side.
Factor out $\phantom{\rule{0ex}{0ex}}secx$:
$\mathrm{sec}x-\mathrm{sec}x{\mathrm{sin}}^{2}x=\mathrm{sec}x\left(1-{\mathrm{sin}}^{2}x\right)$
Use the Pythagorean identity: ${\mathrm{sin}}^{2}x+{\mathrm{cos}}^{2}x=1$
$\mathrm{sec}x-\mathrm{sec}x{\mathrm{sin}}^{2}x=\mathrm{sec}x\left({\mathrm{cos}}^{2}x\right)$
Use the reciprocal identity: $\mathrm{sec}x=1/\mathrm{cos}x$
$\mathrm{sec}x-\mathrm{sec}x{\mathrm{sin}}^{2}x=1/\mathrm{cos}x\left({\mathrm{cos}}^{2}x\right)$
$\mathrm{sec}x-\mathrm{sec}x{\mathrm{sin}}^{2}x=\mathrm{cos}x$