I got this problem to solve: f, g are continious limited functions on R find all solutions to this system f(x+y) = f(x)*f(y)-g(x)*g(y) g(x+y) = f(x)*g(y)+f(y)*g(x) f(0) = 1 g(0) = 0 I only found 1 solution by guessing, and it's g(x) = sin(rx+2pi*n), f(x) = cos(rx+2pi*k), where r is real and n,k are integers Can you please give me the advice how to get more complete solution to this problem or how to prove that there's no more such a function?