
### Instruction: help me answer this question Simplify the expression 2 sin 4x cos (– 2x) + 2 sin 4x, think step by step
### Assistant: Taking common terms, we get 2 sin 4x (cos 2x + 1). Using the formula sin(A + B) = sinA cosB + cosA sinB, we can write cos 2x + 1 as 2cos2 x. Thus, we get 2 sin 4x (2 cos2 x) or 4cos2 x sin 4x. , The answer is 4cos2 x sin 4x
