trigsimp supplement?



Hi, its my first post here.
I don't know what do you mean by 'simpler' but I found:
 
(%i1)L:[-sin(x)^2/(cos(x)^2-1),sin(x)^2/(cos(x)^2-1),1,(cos(x)^2-1)/sin(x)^2,-cos(x)^2/(sin(x)^2-1),cos(x)^2/(sin(x)^2-1),1,(sin(x)^2-1)/cos(x)^2]$
(%i2) load(trigrat);
(%o2)      /usr/share/maxima/5.15.0/share/trigonometry/trigrat.lisp
(%i3) trigrat(L);
(%o3)                  [1, - 1, 1, - 1, 1, - 1, 1, - 1]

Rafal Topolnicki

> I am looking for more power in simplifying expressions
> using cos(x)^2 + sin(x)^2 = 1.
> 
> My candidate so far is:
> 
> ts1(expr):=
>   (trigreduce(expr),trigexpand(%%),trigsimp(%%) )$
> 
> A comparison test is:
> 
> (%i17) display2d:false$
> 
> (%i18) map('trigsimp, [sin(x)^2/(1-cos(x)^2), sin(x)^2/(cos(x)^2-1),
>          (1-cos(x)^2)/sin(x)^2, (cos(x)^2-1)/sin(x)^2, 
> cos(x)^2/(1-sin(x)^2),
>           cos(x)^2/(sin(x)^2-1), (1-sin(x)^2)/cos(x)^2, 
> (sin(x)^2-1)/cos(x)^2]);
> 
> (%o18) [-sin(x)^2/(cos(x)^2-1), sin(x)^2/(cos(x)^2-1), 1, 
> (cos(x)^2-1)/sin(x)^2,
>         -cos(x)^2/(sin(x)^2-1), cos(x)^2/(sin(x)^2-1), 1, 
> (sin(x)^2-1)/cos(x)^2]
> 
> (%i19) map('ts1,[sin(x)^2/(1-cos(x)^2), sin(x)^2/(cos(x)^2-1),
>          (1-cos(x)^2)/sin(x)^2, (cos(x)^2-1)/sin(x)^2, 
> cos(x)^2/(1-sin(x)^2),
>           cos(x)^2/(sin(x)^2-1), (1-sin(x)^2)/cos(x)^2, 
> (sin(x)^2-1)/cos(x)^2]);
> 
> (%o19) [1, -1, 1, -1, 1, -1, 1, -1]
> 
> Is there a simpler way to get the same simplifying power?
> 
> Ted Woollett
> 
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