# How do you evaluate sec^-1(1)?

${\sec}^{-} 1 1 = 0$.
By Defn. ${\sec}^{-} 1 x = \theta , | x | \ge 1 \iff \sec \theta = x , \theta \in \left[0 , \pi\right] - \left\{\frac{\pi}{2}\right\}$
Since, $\sec 0 = 1 , w h e r e , 0 \in \left[0 , \pi\right] - \left\{\frac{\pi}{2}\right\}$, we have, ${\sec}^{-} 1 1 = 0$.