Does $\operatorname{arcsec}(x) = 1 /\arccos(x)$? Does $\operatorname{arcsec}(x) = 1 /\arccos(x)$? I have looked in a few books and Google'd it but I am not finding my answer.

If $\sec^{-1} x = \theta$, then $x = \sec\theta$. This means $\frac1x = \cos\theta$, so $\cos^{-1}\frac1x = \theta$. So your equation is wrong; the correct statement is $$\boxed{\sec^{-1} x = \cos^{-1}\tfrac1x}$$
