I'm trying to simplify an expression, and my guess would be like this:
FullSimplify[Sqrt[1 - Cos[θ]^2/sign[r Cos[ϕ] Sin[θ]]^2], sign[_]^2 == 1]
Apparently, as I get unchanged expression back,
FullSimplify doesn't understand what I mean. (
sign is deliberately not a system
Sign function here).
I do realize that I could simply switch to a replacement like
expr /. sign[_]^2 -> 1, but I suppose in general simplification with a pattern could be more useful. E.g. when
sign[...]^n would have
n==4 or whatever. Also in this case the rule I mentioned wouldn't work, since it should instead be
sign[_]^-2 -> 1 here.
So my question is: how do I use patterns in assumptions of
Simplify family of functions?