# Thread: how cosh(ln(4+sqr(17)) becomes asqrt(17)

1. ## how cosh(ln(4+sqr(17)) becomes asqrt(17)

Hi, at a point Q, x = (4+sqrt(17)

find the y co-ordinate, expressing your answer in surd form

x can also be written arsinh(4)

but I don't know if that helps.

I'm stumped :\
Thanks

2. $\text{cosh} \ x = \frac{e^{x}+e^{-x}}{2}$. And $\text{sinh}^{-1} \ x = \log(x+ \sqrt{x^2+1})$.

3. Hi

$\cosh(\ln(4+\sqrt{17})) = \frac{e^{\ln(4+\sqrt{17})}+e^{-\ln(4+\sqrt{17})}}{2}$

$\cosh(\ln(4+\sqrt{17})) = \frac{4+\sqrt{17}+\frac{1}{4+\sqrt{17}}}{2}$

$\cosh(\ln(4+\sqrt{17})) = \frac{17+4\sqrt{17}}{4+\sqrt{17}}$

$\cosh(\ln(4+\sqrt{17})) = \frac{17+4\sqrt{17}}{4+\sqrt{17}}\:\frac{\sqrt{17}-4}{\sqrt{17}-4}$

$\cosh(\ln(4+\sqrt{17})) = (17+4\sqrt{17})(\sqrt{17}-4) = \sqrt{17}$

4. thank you both very much. it's easy peasy