anonymous
  • anonymous
Help me solve this question please.. Given cosh x = square root 3, find value of cosh 2x
Mathematics
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anonymous
  • anonymous
Help me solve this question please.. Given cosh x = square root 3, find value of cosh 2x
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
By definition of hyperbolic cosine, \[\cosh x=\sqrt3~~\implies~~\frac{e^x+e^{-x}}{2}=\sqrt3~~\implies~~e^{2x}-2\sqrt3e^x+1=0\] which, if we let \(t=e^x\), has roots \[t=\frac{2\sqrt3\pm\sqrt{8}}{2}~~\iff~~x=\ln\frac{2\sqrt3\pm\sqrt8}{2}=\ln(\sqrt3\pm\sqrt2)\] So, knowing this, you can easily determine \(\cosh2x\).
anonymous
  • anonymous
The answer i got is 4.897, is it correct?
anonymous
  • anonymous
The answer i got is 4.897, is it correct?

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anonymous
  • anonymous
Sorry, not cosh 2x, but sinh 2x
anonymous
  • anonymous
Sorry, not cosh 2x, but sinh 2x
anonymous
  • anonymous
Determining \(\sinh2x\) isn't so far off from finding \(\cosh2x\). Just use the definitions: \[\cosh x=\frac{e^x+e^{-x}}{2}\quad\quad\quad\sinh x=\frac{e^x-e^{-x}}{2}\]

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