Anyone know how to solve this Polar Equation

I need to replace this Polar equation with equivalent Cartesian equations. r^2+2r^2cosxsinx=1.

r^2 = x^2 + y^2
sin(t) = y/r
cos(t) = x/r

r^2 + 2*r^2*cos(x)*sin(x) = 1
r^2(1 + 2*cos(x)*sin(x)) = 1
(x^2 + y^2)(1 + 2*cos(x)*sin(x)) = 1
x^2 + y^2 = 1 / (1 + 2*cos(x)*sin(x))
y^2 = (1 / (1 + 2*cos(x)*sin(x))) - x^2
y = +/- sqrt((1 / (1 + 2*cos(x)*sin(x))) - x^2)

Or did you mean:
r^2 + 2*r^2*cos(t)*sin(t) = 1
r^2 + 2r^2(x/r)(y/r) = 1
r^2 + 2xy = 1
x^2 + y^2 + 2xy = 1
(x + y)^2 = 1
x + y = +/- sqrt(1)
x + y = +/- 1
y = -x +/- 1