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