Where is the start of the wrong in these step/s ?

Prove: (sin x)[(cos^3)x] - (cos x)[(sin^3)x] = (1/4)(sin 4x)

Step 1: (sin x)[(cos^3)x] - (cos x)[(sin^3)x] = (1/4)(sin 4x)

Step 2: (sin x)(cos x)[(cos^2)x - (sin^2)x] = (1/4)(sin 4x)

Step 3: (sin x)(cos x)[1-2(sin^2)x] = (1/4)(sin 4x)

Step 4: (sin x)(cos x)(cos 2x) = (1/4)(2sin 2x)(cos 2x)

Step 5: (sin x)(cos x)(cos 2x) = (1/4)(2sin x)(cos x)(cos 2x)

Step 6: 1 = 2 ?

Where is the start of the wrong? :D

Take note: If you get the answer, show your solution/Proof .

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