I need your help math geniouses.
Show that the involute of the catenary parameterized by arc length is a reparametrization of tractrix. (use the change of parameter 1/cosh(t)=sin(r))

The involute of the catenary (with arc lenght param.) gave me the following result:

$\displaystyle (arcsinh(s), cosh(arcsinh(s))) + (s_o - s)$ $\displaystyle (\frac{1}{\sqrt{s^2 + 1}},$ $\displaystyle \frac{s}{\sqrt{s^2 + 1}})$

when I use the change of parameter s = sinh(t) I have this:

$\displaystyle (t,cosh(t)) + (sinh(t_0) - sinh(t)) (\frac{1}{cosh(t)} , tgh(t))$

I dont know how to continue with what its proposed 1/cosh(t)=sin(r) or if everything I did is worong . Please guide me on the path of certainty!!!