Suppose that for all real x S'(x) = -g(x) and g'(x) = f(x). (a) Show that f²(x)+g²(x)= C for some constant C. (b) Suppose that f(0) = 0 and g(0) = 1. What is C? (c) Give an example of a pair of functions that satisfy parts (a) and (b).

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