# How do you find Sec^-1(sec((7pi)/6))?

$= 5 \frac{\pi}{6}$ least value
${\sec}^{-} 1 \left(\sec \left(7 \frac{\pi}{6}\right)\right) = {\sec}^{-} 1 \left(\sec \left(\pi + \frac{\pi}{6}\right)\right) = {\sec}^{-} 1 \left(- \sec \left(\frac{\pi}{6}\right)\right) = {\sec}^{-} 1 \left(\sec \left(\pi - \frac{\pi}{6}\right)\right) = {\sec}^{-} 1 \left(\sec \left(5 \frac{\pi}{6}\right)\right) = 5 \frac{\pi}{6}$