Let m, n be integers with m ≠ ±n. Use Eqs. (15)–(17) to prove the so-called orthogonality relations that play a basic role in the theory of Fourier Series (Figure 1):

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A A J y = sin 2x sin 4x J J T 21 sin mx sin nx dx = 0 cos mx cos nx dx = 0 sin mx cos nx dx = 0 W y = sin 3x cos 4x 21