Let F be the set of functions of the form f(x) = A sin(x) + B cos(2x), where A, B are some real constants. Show that there must

Question

Let F be the set of functions of the form f(x) = A sin(x) + B cos(2x), where A, B are some real constants. Show that there must exist exactly one function f in F so that for any f∈F
√∫(f(x)- arctan(x))²dx≤ √∫(f(x)- arctan(x))²dx

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