This is a worked example from my textbook:
Evaluate these expressions exactly, rationalizing denominators when necessary.
$\sin(\sin^{-1}\frac{4}{5})$
Let $\alpha = \sin^{-1}\frac{4}{5} $
Then $\sin\alpha=\frac{4}{5}$ (where the condition $-\frac{\pi}{2} \le\alpha\le\frac{\pi}{2}$ is now irrelevant.)
The part I don't understand is where they said "the condition $-\frac{\pi}{2} \le\alpha\le\frac{\pi}{2}$ is now irrelevant". Why would the restriction on the domain be lifted for this question?