Express each of the following as a product: `sin4theta+sin2theta` (ii) `sin6theta-sin2theta` (iii) `cos4theta+cos8theta` (iii) `cos6theta-cos8theta`

Explanation

To express the given trigonometric functions as products, we will use specific transformation formulas for sine and cosine. Let's solve each part step by step.

### Part (i): Express `sin 4θ + sin 2θ` as a product

1. **Identify the formula**: We use the formula for `sin A + sin B`, which is:
\[ \sin A + \sin B = 2 \sin\left(\frac{A+B}{2}\right) \cos\left(\frac{A-B}{2}\right) \]
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