Hi Stavros
I slightly misunderstanding this tema.
If some CAS could do this,may be adhoc.
Always exsisting tan(x)=sqrt(3),so
a:(sin(2*%pi/9)+tan(x)*cos(2*%pi/9))/(sin(2*%pi/9)*tan(x)-cos(2*%pi/9))$
trigsimp(a)$
trigreduce(%);
2 %pi 2 %pi
(%o4) - sec(x + -----) sin(x + -----)
9 9
solve tan(x)=sqrt(3),subst this x to (%o4)
how about?
gosei furuya
2006/10/26, ???? <go.maxima at gmail.com>:
>
> Ya macrakis
>
> if first step is possible case,
> I think your problem can be solved in one function.
> example
> simp:false$
> a:cos(%pi/3)*sin(2*%pi/9)+sin(%pi/3)*cos(2*%pi/9))/
> (sin(%pi/3)*sin(2*%pi/9)-cos(%pi/3)*cos(2*%pi/9))$
> subst(['%pi=x],%);
> simp:true$
> trigreduce(%);
> trigsimp(subst([x=%pi],%);
> -sin(5*%pi/9)/cos(5*%pi/9) return.
> generaly transporte %pi --->x,simprule can adapte it.
> after x-->%pi.
> But first step is due to human ??
>
> thanks
> Gosei Furuya
>
>
>
>
>
> 2006/10/26, Stavros Macrakis <macrakis at gmail.com>:
> >
> > Any clever ideas about how to simplify
> >
> >
> > (sin(2*%pi/9)+sqrt(3)*cos(2*%pi/9))/(sqrt(3)*sin(2*%pi/9)-cos(2*%pi/9))
> >
> > to
> >
> > tan(4*%pi/9) ?
> >
> > Thanks,
> >
> > -s
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>