Math Problem Statement
(3\sin x-4\sin ^{3}x)
Solution
The given expression is . This can be recognized as a form of the sine triple angle identity.
The identity is:
Thus, the expression simplifies directly to:
Final Answer:
Would you like further details on how to use this identity in problems?
Related questions:
- What are the other common trigonometric identities?
- How can we derive the triple angle identity?
- Can this identity be used to solve equations involving ?
- How would this identity affect integration or differentiation of trigonometric expressions?
- 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
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