Any help in this problem?

Suppose U and V are independent random variables with density f(u) and g(v) respectively. The domain of U is the interval (0, 1) and the domain of V is v > 0. After the transformation

X = V sin(2U) Y = V cos(2U)

X and Y are independent, each following the standard normal distribution N(0, 1).

(a) Find f(u) and g(v).

(b) Show how to generate a normal random variable from uniform distribution without having to do integration of normal density function.