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

• This Question is Open
1. 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 $$\cosh2x$$.

2. anonymous

The answer i got is 4.897, is it correct?

3. anonymous

The answer i got is 4.897, is it correct?

4. anonymous

Sorry, not cosh 2x, but sinh 2x

5. anonymous

Sorry, not cosh 2x, but sinh 2x

6. anonymous

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