The expression \( \sin^5(2x)\cos(x) \) can be simplified using trigonometric identities, but it doesn't have a direct, simple alternative form. However, it can be expanded or rewritten depending on the context:

One possible approach involves expressing it in terms of powers of \(\sin(2x)\) and using substitution if required. But without additional context or specific instructions (like an integral, derivative, or identity to use), it remains as is.

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Here are some related questions to consider:
1. How do you simplify trigonometric expressions involving powers and products?
2. What identities are useful when combining sine and cosine functions?
3. How does the double-angle identity relate to expressions like \( \sin^2(2x) \)?
4. Can the expression \( \sin^5(2x)\cos(x) \) be expanded using the binomial theorem?
5. How do you integrate products of sine and cosine functions?

**Tip:** When dealing with trigonometric powers, consider using substitution or trigonometric identities to simplify or solve the expressions.

Explore how to simplify the expression \( \sin^5(2x)\cos(x) \) using trigonometric identities. This problem involves understanding trigonometric powers and their relationships, suitable for advanced high school students and anyone interested in trigonometry.

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