'demoivre' not quite up to Wolfram's 'ExpToTrig' ?

I'm trying to 'undo' exponentialize on sinh(x), cosh(x), etc.

While demoivre(exp) works on sin(x), cos(x), it doesn't work on sinh(x), cosh(x).

But you can trick demoivre by substituting x=%i*y, do demoivre, and then substitute back y=x/%i.

Why isn't 'demoivre' smart enough to do this itself ?