Solution
= Solution
Squaring $p_H=p_1+p_2$ gives $m^2c^4=2E_1E_2(1-\cos\theta)=4E_1E_2\sin^2(\theta/2)$, proving the formula. If the rest-frame photons are along $\pm y$, an $x$-boost gives equal energies and $\sin(\theta/2)=1/\gamma$, hence $v=c\cos(\theta/2)$.