1. Show that, when $\theta$ is small, the value of $\sqrt{2}\sec \theta$ may be approximated by a function of the form

   $$f(\theta )=\frac{A}{\theta +\sqrt{2}}+\frac{B}{\theta -\sqrt{2}}$$

   where $A$ and $B$ are integers to be determined.

2. Show that $f(\theta )$ is an even function.

For (a), use the difference of two squares to get