Answer
$\theta$ lies in quadrant IV
Work Step by Step
Given
$\sec\theta \gt 0$ i.e. $\sec\theta$ is positive.
$\tan\theta \lt 0$ i.e. $\tan\theta$ is negative.
$\sec$ is positive and $\tan$ is negative in quadrant IV only, therefore-
$\theta$ lies in quadrant IV
