# How do you evaluate sec^-1(sec((7pi)/10))?

$\frac{7 \pi}{10}$
${\sec}^{- 1} x$ is defined for x$\in \left(R -\right] - 1 , 1 \left[\right) \rightarrow \left(\left[0 , \pi\right] - \left\{\frac{\pi}{2}\right\}\right)$.
${\sec}^{- 1} \sec x = x$ if and only if x$\in \left(\left[0 , \pi\right] - \left\{\frac{\pi}{2}\right\}\right)$.
in your question, since $\frac{7 \pi}{10} \in \left(\left[0 , \pi\right] - \left\{\frac{\pi}{2}\right\}\right)$
so, ${\sec}^{- 1} \sec \left(\frac{7 \pi}{10}\right) = \frac{7 \pi}{10}$