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.
Or, directly from the definition, since $\displaystyle sinh(\theta)= \frac{e^{\theta}- e^{-\theta}}{2}$,
$\displaystyle sinh^2(\theta)= \frac{e^{2\theta}- 2+ e^{-2\theta}}{4}= \frac{e^{2\theta}+ e^{-2\theta}}{4}- \frac{1}{2}$ so
$\displaystyle 2sinh^2(\theta)= \frac{e^{2\theta}+ e^{-2\theta}}{2}-1$ and then
$\displaystyle 2sinh^2(\theta)+ 1= \frac{e^{2\theta}+ e^{-2\theta}}{2}= cosh(2\theta)$.