Express each of the following as a sum of difference of sine and cosine.
i) `2sin2A cosA`
ii) `2cos5Asin2A`
iii) `2cos4AcosA`
iv) `2sin3AsinA`

Explanation

Let's solve the given expressions step by step.

### i) \( 2 \sin 2A \cos A \)

**Step 1:** Identify the formula to use.
The formula for \( 2 \sin a \cos b \) is:
\[
2 \sin a \cos b = \sin(a + b) + \sin(a - b)
...