In this problem we will prove one orthogonality relation used in Fourier analysis. a) Show that sin(mx) cos(nx) = ½ (sin((m +n)x) + sin((m − n)x)) using the angle addition and subtraction formulas. b) Use the result from part a) to evaluate the integral [ε sin (mx) cos(nx) dx c) Prove the following statement for integers m‡±n. (y = sin 3x cos 4x is graphed for reference) 2π sin(mx) cos(nx) dx = 0 որիան, M

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