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sin(4x)cos(8x)-cos(4x)sin(8x)=-.4      for smallest positive solution

 Jun 12, 2020
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sin(4x)cos(8x)-cos(4x)sin(8x)=-.4      for smallest positive solution

 

Hello carlos!

 

\(sin(4x)cos(8x)-cos(4x)sin(8x)=-0.4 \)

 

\(sin(\alpha-\beta)=sin(\alpha)cos(\beta)-cos(\alpha)sin(\beta)\ \color{black}\small{(Bartsch\ Leipzig\ 1980)}\)

    \(\alpha=4x\\ \beta =8x\)

\(sin(4x-8x)=sin(4x)cos(8x)-cos(4x)sin(8x)=-0.4\)

   \(sin(-4x)=-0.4\)

  \(-4x=arcsin(-0.4)\\ x= \frac{arcsin(-0.4)}{-4}\)

  \(x=0.102879211517\)

laugh  !

 Jun 13, 2020
edited by asinus  Jun 13, 2020

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