I'm stuck on a proof of the following:

S and S' are the foci of the hyperbola with equation x^2/a^2 - y^2/b^2 = 1.

Show that SP and S'P are equally inclinled to the tangent at any point P on the hyperbola.

I've worked out the gradients for the tangent as (b sec t) / (a tan t); the line SP as (b tan t)/(a sec t - ae); S'P as (b tan t)/(a sec t + ae). I don't know where to go from there.