
### Instruction: help me answer this question Prove that cos2 2x – cos2 6x = sin 4x sin 8x, think step by step
### Assistant: Using sum and difference formulas, cos 6x can be written as cos (2x + 4x) and cos 4x can be written as cos (2x + 2x). Then applying the formula for cos (a + b) and cos (a - b) and using some trigonometric identities, the result can be obtained. , The answer is cos2 2x – cos2 6x = sin 4x sin 8x
