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