Answer
$30^{\circ}, 330^{\circ}$
Work Step by Step
Given $\sqrt 3\sec\theta$=2 .....(1)
As we know that $\sec\theta$ is the reciprocal of $\cos\theta$
so we can write as $\sec\theta = \frac{1}{\cos\theta}$ .....(2)
Substitute (2) in equation (1) we get
$\sqrt 3(\frac{1}{\cos\theta})$=2
$\sqrt 3=2\cos\theta$
On dividing both the sides by 2
$\frac{\sqrt 3}{2}= \cos\theta$
$\theta = 30^{\circ}$
cosine function is positive in quadrant 1 & 4
$\theta=30^{\circ} $ or $\theta^{\circ} = 360^{\circ}-30$
$\theta=30^{\circ} $ or $\theta^{\circ} = 330^{\circ}$
