I have this question in a exam in which you have to choose only one of the possible answers: What would be correct?
Let be $ f,g : \mathbb{R} \rightarrow \mathbb{R} $ two derivable functions such that f'(x)=g(x),g'(x)=f(x),f(0)=1,g(0)=0 . And let be the function $F(x)=f^2(x)+g^2(x)$, then:
a) $F(x)=1-\sin(x)$.
b) $F$ is the constant function with value 1.
c) None of the other two answers.
Frankly I don't even know where to start and the possible relationship between the conditions and possible responses.