> It makes sense to me. I think I would add a transform that looks for
> `cos(x) - I*sin(x)`, kind of a special induced formula. Should
> `cos(x) + I*sin(x)` go to `exp(I*x)`, too?

Maxima has a special command for that sort of transformations:

```
(%i1) exponentialize(sin(x)+cos(x));
                    %i x     - %i x         %i x     - %i x
                  %e     + %e         %i (%e     - %e      )
(%o1)             ----------------- - ----------------------
                          2                     2

(%i2) exponentialize(sinh(x)+cosh(x));
                             x     - x     x     - x
                           %e  + %e      %e  - %e
(%o2)                      ----------- + -----------
                                2             2

(%i3) exponentialize(cos(x)-%i*sin(x));
                       %i x     - %i x     %i x     - %i x
                     %e     + %e         %e     - %e
(%o3)                ----------------- - -----------------
                             2                   2

(%i4) exponentialize(cos(x)+%i*sin(x));
                       %i x     - %i x     %i x     - %i x
                     %e     + %e         %e     - %e
(%o4)                ----------------- + -----------------
                             2                   2
```