Chapter 5 - Section 5.5 - Trigonometric Equations - Exercise Set - Page 704: 83

$x=0$

Step 1. Using the identity $sec^2x=1+tan^2x$, rewrite the equation as $sec(x)=1-tan(x)$ and take the square on both sides to get $sec^2x=1+tan^2x-2tan(x)$; thus we have $tan(x)=0$ Step 2. For $tan(x)=0$, we can find all x-values in $[0,2\pi)$ as $x=0,\pi$ Step 3. Checking the above with the original equation, we can find $x=0$ as the only answer.