That distribution doesn't make sense for the reasons you described. If you look at
https://en.wikipedia.org/wiki/Box%E2...ller_transform under the polar form (2 * uniform[0,1] - 1 is uniform [-1,1] obviously), the last part of the calculation is identical to the "otherwise" in yours.... but that's intended for cases where your s^2<1 inequality holds. Are you sure you aren't misreading the question and adding an "otherwise" that doesn't belong and that's actually supposed to be the definition of x as a standard normal deviate?
