Consider the set {sin2 x, cos2 x} in the vector space of differentiable real-valued functions. Determine which of the following functions are in the span of the above set: f(x) = 1, g(x) = 3 + x2, h(x)

Consider the set {sin2 x, cos2 x} in the vector space of differentiable real-valued

functions. Determine which of the following functions are in the span of the
above set: f(x) = 1, g(x) = 3 + x2, h(x) = sin x and k(x) = cos 2x.

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