I am using maple to verify an expression, $x < \tan(x)$ for $0 < x < \pi/2$, but it returns FAIL, i.e.
is ( x < tan(x) ) assuming 0 < x < Pi/2
which returns FAIL.
I am very curious to know why this in-equality cannot be evealuated by Maple? I can evaluate is by computing the following
f := x -> tan(x) - x
g := x -> diff(f(x), x)
is (g(x) > 0) assuming 0 < x < Pi/2
which returns true.
Note1: Maple uses 3-valued logic for boolean operations, true, false and FAIL, where FAIL is returned whenever Maple is unable to evaluate a proposition with certainty.
Note2: Maple is a proprietary computer algebraic system that I have access through my university's lab.