Error parameter of fit function

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I have the following function:
f(x)/2=A cos(x)

I used a “cos” fitting function and I obtain the fit parameter (A) and the error of fit parameter.
Another time I used the following function

f(x)=2A cos(x)

The fit parameter shows 2A and the error parameter was obtained. I expected the same value of error parameters for these two functions but they are different. I don’t know which one is correct. Please help me.

Thanks in advance

I’m not sure to understand what you’re asking for, maybe @moneta has some hints…

Thanks for your answer,
In fact I want to know how the error parameter of fitted histogram compute in root. I have a sum of two functions divided by 2, (f1+f2)/2, and I fitted a “A cos” function on it. Another time I used f1+f2 and I fitted “2A cos” function on it. In these two method the error parameters was different. I expected the same error parameter because “2” is a constant value. I don’t know the role of “2” in the error parameter.

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