Costa,
Thanks for your wishes for 2008 -- the same to you!
Its not clear why trigsimp() introduces a singularity in Maxima 5.10/5.12
> but
> seemingly not in Maxima 5.13.99.
There are many algebraic transformations which are correct in general but
incorrect at individual points. Maxima isn't careful about that (for
example, it simplifies x/x to 1 without the proviso that x <> 0 -- in fact
there is no mechanism for "provisos" like this), so I'm not surprised that
various simplification functions should introduce removable singularities as
well as remove them without notice.
Version 5.13 apparently changes the behavior in this particular case, but
for all I know may introduce other cases.
Why don't ratsimp/radcan remove removable singularities in general? Because
they only know about algebraic functions, not trigonometric ones.
-s