Q is distributed uniformly on [0,2pi]

W and Q are independent.

R=sqrt(2W)

-pi/2<=a<=pi/2 - constant.

U=Rcos(Q)

V=Rsin(Q+a)

Need to prove (U,V) has bivariate normal distribution with correlation equal to sin(a)

Its hard for me to solve it, I tried to find joint distribution of (U,V), but to find this you need to integrate the joint distribution of (W,Q) on complex regions, it is practically impossible. Also I tried to find m.g.f and c.f. of vector (U,V) to show it is Gaussian, but I cant take needed integrals too.

Have someone idea how to solve this?