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anonymous
 one year ago
Help me solve this question please.. Given cosh x = square root 3, find value of cosh 2x
anonymous
 one year ago
Help me solve this question please.. Given cosh x = square root 3, find value of cosh 2x

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0By 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
 one year ago
Best ResponseYou've already chosen the best response.0The answer i got is 4.897, is it correct?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The answer i got is 4.897, is it correct?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Sorry, not cosh 2x, but sinh 2x

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Sorry, not cosh 2x, but sinh 2x

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Determining \(\sinh2x\) isn't so far off from finding \(\cosh2x\). Just use the definitions: \[\cosh x=\frac{e^x+e^{x}}{2}\quad\quad\quad\sinh x=\frac{e^xe^{x}}{2}\]
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