Chapter 13.9, Problem 1P

Verify that (9.15) follows from $(9.14).$ Hint: Use the formulas for $\tan (\alpha \pm \beta ),\tan 2\alpha$ etc., to condense (9.14) and then change to polar coordinates. You may find $u=\frac{100}{\pi }\arctan \frac{\sin 2\theta }{r^2-\cos 2\theta }$.

Show that if you use principal values of the arc tangent, this formula does not give the correct boundary conditions on the $x$ axis, whereas (9.15) does.