We need to verify the trigonometric identity:
[tex]\begin{gathered} \frac{1}{\sec(x)+\tan(x)}+\frac{1}{\sec(x)-\tan(x)}=\frac{\sec (x)+\tan (x)+\sec (x)-\tan (x)}{(\sec (x)+\tan (x))(\sec (x)-\tan (x))} \\ \frac{1}{\sec(x)+\tan(x)}+\frac{1}{\sec(x)-\tan(x)}=\frac{2\sec (x)}{\sec ^2(x)-\tan ^2(x)} \\ \frac{1}{\sec(x)+\tan(x)}+\frac{1}{\sec(x)-\tan(x)}=2\sec (x) \end{gathered}[/tex]
