[Maxima] trigsimp supplement?

Edwin Woollett woollett at charter.net
Sat Aug 23 15:00:42 CDT 2008

```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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