$\text{The least value of }\left(1+se{c}^{-1}x\right)\left(1+{\cos }^{-1}x\right)\text{is}$

$\text{given expression is defind only for x=1 and x=-1}$

$f\left(x\right)=1 and f\left(-1\right)=\left(1+\pi \right)\left(1+\pi \right)={\left(1+\pi \right)}^2$

$\text{hence least value is 1}$