# Solve the Equation sin x-cos x=1

Solve the Equation
$\mathrm{sin}x-\mathrm{cos}x=1$
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Jazmin Bryan
$\mathrm{sin}x-\mathrm{cos}x=1$
divide by $\sqrt{2}$
$1/\sqrt{2}\mathrm{sin}x-1/\sqrt{2}\mathrm{cos}x=1/\sqrt{2}$
$\mathrm{sin}x·\mathrm{cos}\left(\pi /4\right)-\mathrm{cos}x·\mathrm{sin}\left(\pi /4\right)=1/\sqrt{2}$
$\mathrm{sin}\left(x-\pi /4\right)=1/\sqrt{2}$
$x-\pi /4=\pi /4+2\pi n$
$x=\pi /2+2\pi n$
or
$x-\pi /4=3\pi /4+2\pi k$
$x=\pi +\pi k$