Final answer:
To simplify the expression, we recognize that it is squared. Thus, the simplified form is (cos3x sin2x cosx)^2, and no further simplification or identities are required.
Step-by-step explanation:
To simplify the expression cos3x sin2x cosx cos3x sin2x cosx, we look for basic trigonometric identities that can be applied. From the provided information, we identify the double angle identities (like the ones for cos 2θ), which can be potentially useful. However, as given, we already have a product of cosines and sines with the same angles, which simplifies directly.
In this case, we can square the given expression:
- cos3x sin2x cosx × cos3x sin2x cosx = (cos3x sin2x cosx)2
This simplification highlights that we are dealing with the square of the entire expression. The initial expression essentially multiplies by itself. We can skip looking for more complicated identities since the given expression doesn't need them to simplify further. Instead, we end with:
- The final simplified form is (cos3x sin2x cosx)2.
In this solution, the provided trigonometric identities, like those involving double angles or sum and difference identities, were not necessary for the simplification process.