Chapter 6 - Inverse Circular Functions and Trigonometric Equations - Section 6.3 Trigonometric Equations II - 6.3 Exercises - Page 280: 53

$x = 0.4636~~$ or $~~x=3.6052$

$tan~2x+sec~2x = 3$ $tan~2x= 3-sec~2x$ $tan^2~2x= 9-6~sec~2x+sec^2~2x$ $sec^2~2x-1= 9-6~sec~2x+sec^2~2x$ $6~sec~2x= 10$ $sec~2x= \frac{5}{3}$ $cos~2x= \frac{3}{5}$ $2x = 0.9273~~$ or $~~2x=7.2105$ $x = 0.4636~~$ or $~~x=3.6052$