The given expression is \( 3\sin x - 4\sin^3 x \). This can be recognized as a form of the **sine triple angle identity**.

The identity is:
\[
\sin(3x) = 3\sin x - 4\sin^3 x
\]

Thus, the expression \( 3\sin x - 4\sin^3 x \) simplifies directly to:
\[
\sin(3x)
\]

### Final Answer:
\[
3\sin x - 4\sin^3 x = \sin(3x)
\]

Would you like further details on how to use this identity in problems?

### Related questions:
1. What are the other common trigonometric identities?
2. How can we derive the triple angle identity?
3. Can this identity be used to solve equations involving \( \sin(3x) \)?
4. How would this identity affect integration or differentiation of trigonometric expressions?
5. How do you apply similar identities to different trigonometric functions like cosine?

**Tip:** Remember, triple angle identities help reduce higher powers of sine or cosine, simplifying complex expressions.

Learn how to simplify the trigonometric expression 3sin(x) - 4sin^3(x) by applying the sine triple angle identity. This step-by-step solution is suitable for high school students in Grades 10-12 studying advanced trigonometry concepts.

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