\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
In \(\mathbb{R}^\mathbb{R}\) (the \(\mathbb{R}\)-vector space of functions \(\mathbb{R} \to \mathbb{R}\)), is the function \(x \mapsto \cos^2 x\) a linear combination of the constant function \(x \mapsto 1\) and the function \(x \mapsto \cos(2x)\)?
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