# Math Help - hyperbolics!

1. ## hyperbolics!

can someone offer advise with this one please?

prove: cosh 2theta=2sinh^2 theta + 1

can anyone advise how to resolve this one honestly dont know where to start with it.

thankyou

any pointers appreciated.

2. Originally Posted by ads114
can someone offer advise with this one please?

prove: cosh 2theta=2sinh^2 theta + 1

can anyone advise how to resolve this one honestly dont know where to start with it.

thankyou

any pointers appreciated.

$\cosh{2\theta} = \cosh^2{\theta} + \sinh^2{\theta}$

$= 1 + \sinh^2{\theta} + \sinh^2{\theta}$

$= 2\sinh^2{\theta} + 1$

3. Or, directly from the definition, since $sinh(\theta)= \frac{e^{\theta}- e^{-\theta}}{2}$,

$sinh^2(\theta)= \frac{e^{2\theta}- 2+ e^{-2\theta}}{4}= \frac{e^{2\theta}+ e^{-2\theta}}{4}- \frac{1}{2}$ so

$2sinh^2(\theta)= \frac{e^{2\theta}+ e^{-2\theta}}{2}-1$ and then

$2sinh^2(\theta)+ 1= \frac{e^{2\theta}+ e^{-2\theta}}{2}= cosh(2\theta)$.