How do you simplify tan(cos^(-1)x)?

Let $a = {\cos}^{- 1} x$. Then $x = \cos a \mathmr{and} \tan a = \sin \frac{a}{\cos} a = \pm \left(\frac{\sqrt{1 - {x}^{2}}}{x}\right)$
Answer:$\pm \left(\frac{\sqrt{1 - {x}^{2}}}{x}\right)$