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 $$f^{\prime}(0)=0,$ prove that $(f(x))^{2}+(g(x))^{2}=1$ for all $x$$

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## Video Transcript

the question here. This weather, the integral next time is jail Baxter Yanks. Does he continue in a girl that works? Sorry. You know, grow of flex, Jax. Me times in a row. Three events, Jax. But I think that this is false. Why? Hello. Think to the cast and function. Creed backs inconstant 100 0 I mean, no max times to your folks. Jax is the integral 02 Yet this is just a constant animation. See? And the girl Relax. Yeah, thanks. Turns, you know, Max. Thanks. Yes, thanks. Close some Constantine times, some constant C. Some of these I'm not evil. Who could make sense?

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