Math Problem Statement

(3\sin x-4\sin ^{3}x)

Solution

The given expression is 3sinx4sin3x3\sin x - 4\sin^3 x. This can be recognized as a form of the sine triple angle identity.

The identity is: sin(3x)=3sinx4sin3x\sin(3x) = 3\sin x - 4\sin^3 x

Thus, the expression 3sinx4sin3x3\sin x - 4\sin^3 x simplifies directly to: sin(3x)\sin(3x)

Final Answer:

3sinx4sin3x=sin(3x)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)\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.

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Angle Identities

Formulas

Triple Angle Identity: sin(3x) = 3sin(x) - 4sin^3(x)

Theorems

Sine Triple Angle Identity

Suitable Grade Level

Grades 10-12