(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

suppose f and g are two differentiable functions with f(0)=0, g(0)=1 and f'(x)=g(x) and g'(x)=-f(x). For a fixed y in R put

F(x) = f(x+y) - f(x)f(y) - g(x)f(y)

Compute F'(x) and F''(x)

Then let

E(x) = [F(x)]^2 + [F'(x)]^2

Apply Mean Value Theorem to E and hence prove the addition formulae for f(x+y) and g(x+y)

2. Relevant equations

3. The attempt at a solution

I don't think what I've computed it correct, can anyone kindly please check?

http://img192.imageshack.us/img192/5237/rimg0036.jpg [Broken]

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# Homework Help: Addition formula for f(x+y) using mean-value theorem

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