Tractrix Reparametrization.

[kezman]

I need your help!.
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:

(arcsinh(s), cosh(arcsinh(s))) + (s_o - s) (1\sqrt(s^2 + 1)), (s\sqrt(s^2 + 1)))

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

(t,cosh(t)) + (sinh(t_0) - sinh(t)) (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 .
Thanks.