Past exam of the relativity course of the University of Cambridge / 2022 / Section B / 6 / b / ii / Solution

The Lorentz transformation is $t^{\prime }=\gamma (t-vx)$, $x^{\prime }=\gamma (x-vt)$ in units $c=1$. Adding and subtracting givesSince $\gamma (1+v)=\sqrt{(1+v)/(1-v)}$ and the other factor is its reciprocal,Here $\eta$ is the boost rapidity. Their product is unchanged, as required by invariance of the Minkowski interval.