Chapter 6 - Inverse Circular Functions and Trigonometric Equations - Section 6.2 Trigonometric Equations I - 6.2 Exercises - Page 267: 14

$x = \frac{\pi}{3}, \frac{5 \pi}{3}$

$2 \sec x + 1 = \sec x + 3$ $2 \sec x - \sec x = 3 - 1$ $\sec x = 2$ $\frac{1}{\cos x} = 2$ $1 = 2 \cos x $ $\cos x= \frac{1}{2}$ $x = \frac{\pi}{3}, \frac{5 \pi}{3}$ $= 2\pi - \frac{\pi}{3}$ $= \frac{6\pi}{3}- \frac{\pi}{3}$ $= \frac{5 \pi}{3}$