1. The problem statement, all variables and given/known data Suppose f:R→R and g:R→R are both differentiable and that f'(x)=g(x) and g'(x)=-f(x) for all x ∈ R; f(0)=0 and g(0)=1. Prove : (f(x))²+(g(x))²=1 for all x ∈ R. 2. Relevant equations 3. The attempt at a solution I know I need the find d/dx[f(x)²+g(x)²]=d/dx, but I am not sure what that is going to help me find and how to use the result.