2n The space is C[0,21] and the inner product is (f.g) = f(t)g(t) dt. Show that sin mt and sin nt are orthogonal for any positive integers m and n when m n. Begin by writing the inner product using...

Extracted text: 2n The space is C[0,21] and the inner product is (f.g) = f(t)g(t) dt. Show that sin mt and sin nt are orthogonal for any positive integers m and n when m n. Begin by writing the inner product using the given functions. 2x (sin mt, sin nt) = | O at