Why does applying trigsimp aid solvability?

2009/6/11 Stavros Macrakis <macrakis at alum.mit.edu>:
> On Thu, Jun 11, 2009 at 4:20 PM, Paul Richards <paul.richards at gmail.com>
> wrote:
>>
>> PS. How do I better copy/paste maxima output into email? ?I have a
>> feeling this is only viewable with fixed width fonts.
>
> If you set
> ?? display2d:false$
> you will get output that doesn't depend on fixed-width fonts etc.
>

Thanks.

Here are those expressions again:

(%i2) c^2 = (cos(a/r) - 1)^2 + sin(a/r)^2;

(%o2) c^2 = sin(a/r)^2+(cos(a/r)-1)^2
(%i3) solve(%i2, a);

(%o3) [sin(a/r) = -sqrt(-cos(a/r)^2+2*cos(a/r)+c^2-1),
       sin(a/r) = sqrt(-cos(a/r)^2+2*cos(a/r)+c^2-1)]
(%i4) solve(trigsimp(%i2), a);

solve: using arc-trig functions to get a solution.
Some solutions will be lost.
(%o4) [a = (%pi-acos(c^2/2-1))*r]


So my question is still, why does applying "trigsimp" give be a better
answer from "solve"?

-- 
Paul Richards