Question

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

Answer 1

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 \(\cosh2x\).

Answer 2

The answer i got is 4.897, is it correct?

Answer 3

The answer i got is 4.897, is it correct?

Answer 4

Sorry, not cosh 2x, but sinh 2x

Answer 5

Sorry, not cosh 2x, but sinh 2x

Answer 6

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