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## Homework Statement

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.

## Homework Equations

## The Attempt at a Solution

I know I need the find d/dx[f(x)²+g(x)²]=d/dx[1], but I am not sure what that is going to help me find and how to use the result.