Question

Suppose f and g are nonconstant, dierentiable, real-valued functions on R. Furthermore,
suppose that for each pair of real numbers x and y, f(x + y) = f(x)f(y) 􀀀 g(x)g(y) and
g(x+y) = f(x)g(y)+g(x)f(y). If f0(0) = 0, prove that [f(x)]2+[g(x)]2 = 1 for all x.