# [Maxima] Why does applying trigsimp aid solvability?

Paul Richards paul.richards at gmail.com
Thu Jun 11 15:20:27 CDT 2009

```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
```