Chapter 14.11, Problem 23MP

Verify the formulas in Problem 21 to 27 by contour integration or as indicated. Assume $a>0,m>0.$

${\displaystyle {\int }_0^{2\pi }\frac{\sin \theta d\theta }{a+b\sin \theta }}={\displaystyle {\int }_0^{2\pi }\frac{\cos \theta d\theta }{a+b\cos \theta }}=\frac{2\pi }{b}\left(1-\frac{a}{\sqrt{a^2-b^2}}\right),\left|b\right|<a$