Suppose $f$ and $g$ are non-constant, differentiable, real- valued functions defined on $(-\infty, \infty) .$ 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 $$f^{\prime}(0)=0,$ prove that $(f(x))^{2}+(g(x))^{2}=1$ for all $x$$

## Discussion

## Video Transcript

to the statement's true. There's proof. I'm gonna set Max. You too, Max. No. Minus deluxe shoes? No thanks. Max Linus the mother Intendant. Max the ex integrations. Linear. So vax, Linus. No, thanks. Thanks. Which is the general? Who? Zero, Jax. Because just some constant. So that means, But minus three attacks in the constant. That means the death of Max Seaport to you, Max, cause some constant. That makes sense.

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