How do you evaluate sec^-1(sec(-(pi)/6))?

Jul 11, 2016

$- \frac{\pi}{6}$

Explanation:

successive operations by a function f and its inverse #f^(-1), either

way, on an operand, returns the operand.

Here, f is $\sec$, ${f}^{- 1}$ is ${\sec}^{- 1}$ and the operand is $- \frac{\pi}{6}$..

So, ${\sec}^{- 1} \sec \left(- \frac{\pi}{6}\right) = - \frac{\pi}{6}$.