cos 5x - cos 3x = -8 sin? x(2 cos3 x - cos x) Working with the left-hand side, use a Sum-to-Product Identity, and then simplify. LHS = cos 5x - cos 3x 5x + 3x = -2 sin D(sin x) Repeatedly use the Double-Angle Identities, and then simplify by grouping like terms. LHS = -2 . 2 Isin x - Jin x) = -4 · (2(sin x cos x) = -8 (sin? x)( cos X

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