Verify the identity. 2 cos 3x sin x = 2 sin x cos x – 8 cos x sin3 x Working with the left-hand side, use a Product-to-Sum Identity, and then simplify. LHS = 2 cos 3x sin x 2. (sin(3x + x) - - sin 2x Use a Double-Angle Identity for the first term, and then simplify by grouping like terms. LHS = sin 2x = (sin 2x)( Use the Double-Angle Identities as needed, and then simplify by finding the product. |) (21 - 2 sin? x) – 1) LHS = 8 cos x sin x - 2 sin x cos x II

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