Why does applying trigsimp aid solvability?



I have an equation, which I have been solving using Maxima.  What I
don't understand is that "solve" on its own doesn't seem to solve the
whole problem, but "solve(trigsimp(..))" does.

Why is this?



(%i1) c^2 = (cos(a/r) - 1)^2 + sin(a/r)^2;
                          2      2 a         a      2
(%o1)                    c  = sin (-) + (cos(-) - 1)
                                   r         r
(%i2) solve(%i1, a);
           a                2 a          a     2
(%o2) [sin(-) = - sqrt(- cos (-) + 2 cos(-) + c  - 1),
           r                  r          r
                                      a              2 a          a     2
                                  sin(-) = sqrt(- cos (-) + 2 cos(-) + c  - 1)]
                                      r                r          r
(%i3) solve(trigsimp(%i1), a);

solve: using arc-trig functions to get a solution.
Some solutions will be lost.
                                           2
                                          c
(%o3)                    [a = (%pi - acos(-- - 1)) r]
                                          2


PS. How do I better copy/paste maxima output into email?  I have a
feeling this is only viewable with fixed width fonts.

-- 
Paul Richards