Tricky Trig Identity: Solving sin(3x)cos(x)=sin(x)cos(x)(3-sin^2(x))

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Discussion Overview

The discussion centers around the equation sin(3x)cos(x) = sin(x)cos(x)(3 - sin^2(x)), exploring its validity as a trigonometric identity. Participants are examining the equation through various mathematical approaches, including addition formulas and expansions.

Discussion Character

  • Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant expresses difficulty with the equation and seeks assistance, suggesting attempts with addition formulas and expansions.
  • Another participant challenges the validity of the equation by providing a counterexample with x = π/4, implying the equation does not hold for all values.
  • A third participant emphasizes that an identity must be valid for all values, reinforcing the earlier challenge to the equation's validity.
  • A later reply proposes a corrected form of the equation, stating it should be cos(x)sin(3x) ≡ cos(x)sin(x)(3 - 4sin^2(x)), suggesting a potential error in the original formulation.

Areas of Agreement / Disagreement

Participants do not appear to agree on the validity of the original equation, with multiple competing views regarding its correctness and a proposed correction to the identity.

Contextual Notes

The discussion highlights the importance of verifying trigonometric identities across all values, as well as the potential for misinterpretation or error in the formulation of such identities.

relativitydude
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This is a tricky one, sin(3x)cos(x)=sin(x)cos(x)(3-sin^2(x))

I have tried addition formulas and expanding sin(3x) into something else, any help?
 
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That's not just "tricky", it's false! Try [tex]x= \frac{\pi}{4}[/tex].
 
Like Halls said, remember that an identity is an equation that all values are solutions.
 
It should have been

[tex]\cos x\sin 3x\equiv \cos x\sin x\left(3-4\sin^{2}x\right)[/tex]

Daniel.
 

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