An expression (1 / sin² A - 1) where 0 < A <= 90 degrees.

Recall the fundamental trigonometric identity $1 + \cot^2 A = \csc^2 A$. By rearranging it, we get $\csc^2 A - 1 = \cot^2 A$.

Many students confuse $\frac{1}{\sin^2 A}$ with $\cos^2 A$, whereas $\frac{1}{\sin A} = \csc A$.

Always remember the three main Pythagorean identities: $\sin^2 A + \cos^2 A = 1$, $1 + \tan^2 A = \sec^2 A$, and $1 + \cot^2 A = \csc^2 A$. These are frequently tested in competitive exams to simplify complex trigonometric fractions.