Chapter 11.12, Problem 17P

Write the integral in equation (12.7) as an elliptic integral and show that (12.8) gives its value. Hints: Write $\cos \theta =1-2{\sin }^2(\theta /2)$ and a similar equation for cos $\alpha$ Then make the change of variable $x=\sin (\theta /2)/\sin (\alpha /2)$.