Answer
$y-x=1$
Work Step by Step
Formulas relating rectangular $(x,y)$ and polar $(r,\theta)$ coordinates:
$ x=r\cos\theta$ and $ y=r\sin\theta$
$r^{2}=x^{2}+y^{2}$ and $\displaystyle \tan\theta=\frac{y}{x}$.
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$r=\displaystyle \frac{1}{\sin\theta-\cos\theta}$
... divide both sides with r ...
$1=\displaystyle \frac{1}{r(\sin\theta-\cos\theta)}$
$1=\displaystyle \frac{1}{r\sin\theta-r\cos\theta}$
... use $ x=r\cos\theta$ and $ y=r\sin\theta$ ...
$1=\displaystyle \frac{1}{y-x}\qquad/\times(y-x)$
$y-x=1$
