SolveByNamingAnInverseSineOfASineLinearOnEachInterval​(AngouriMath.​Entity,​AngouriMath.​Entity.​Variable,​System.​Boolean)

An inverse sine of a sine of a linear L = a + k x is s k x + c on each interval
where cos(L) keeps its sign, with s = cos(L)/sqrt(cos(L)^2) that sign and c constant there, and an inverse cosine of a cosine the same with the sign of sin(L):
the derivative of asin(sin(L)) is k cos(L)/sqrt(1 - sin(L)^2). Named so, with
s and c standing for those, x/asin(sin(x)) is the rational function
x/(s x + c), which the rules answer, where the inverse sine was an atom no rule read past
a polynomial beside it. The answer is the generic case's on every interval, as
SolveByNamingALogarithmLinearInTheVariable(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean)'s is, and a whole power of s in
it is 1 or s. Real x only: off the real line the sign is not constant
anywhere. Rubi's 5.1.5. Asked as a question of its own.
https://github.com/asc-community/AngouriMath/issues/718