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

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The equation sin(3x)cos(x) = sin(x)cos(x)(3-sin^2(x)) is identified as problematic, with suggestions to use addition formulas and expand sin(3x). A key point made is that the identity should be correctly expressed as cos(x)sin(3x) ≡ cos(x)sin(x)(3-4sin^2(x)). The discussion emphasizes that an identity must hold true for all values of x, illustrating this with the example x = π/4. Overall, the conversation highlights the importance of verifying trigonometric identities for accuracy.
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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 x= \frac{\pi}{4}.
 
Like Halls said, remember that an identity is an equation that all values are solutions.
 
It should have been

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

Daniel.
 

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