Converting Polar to Cartesian Equations

Hi there!

Im a little stuck on one of my questions and was hoping for a little bit of help.. So first, the question

Convert from polar to cartesian form, using double angle formula:

$\displaystyle r=\sqrt{1+cos2\theta}$

Ok, so things that I know:

$\displaystyle r^2=\sqrt{x^2+y^2}$

$\displaystyle x = r cos\theta$

$\displaystyle y = r sin\theta$

The double angle formula which is reffered to, i believe is

$\displaystyle cos2\theta = cos^2 \theta sin^2 \theta$

But i could be wrong

The furthest i have got to in the problem so far is

$\displaystyle r^2 = 1+cos^2 \theta sin^2 \theta$

And now im greatful if anyone is able to help me out please?

Thanks in advance!