Answer
$x^2 + y^2 - x - y = 0$
Work Step by Step
$r = sin\theta + cos\theta$
$r\cdot r = r(sin\theta + cos\theta)$ (multiply both sides by r)
$r^2 = rsin\theta + rcos\theta$
$x^2 + y^2 = y + x$ (since $r^2 = x^2 + y^2$, $x = rcos\theta$ and $y = rsin\theta$)
$x^2 + y^2 - x - y = 0$
The equivalent equation in rectangular coordinates is $x^2 + y^2 - x - y = 0$
