Question: Consider the vector space of continuous real-valued functions on [0, ] with an inner product defined by (f, g) = 0 f(t)g (t)dt. Show that

Consider the vector space of continuous real-valued functions on [0, π] with an inner product defined by (f, g) = ∫π0 f(t)g (t)dt. Show that the collection of functions sin nt, for n = 1, 2.... is an orthogonal set.

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