 Solution

Generate independent standard normal variables $Z_1,Z_2$ and put $\boxed{Y=Z_1/Z_2}$. The event $Z_2=0$ has probability zero. The ratio calculation in M4 with equal standard deviations gives density $1/[\pi (1+y^2)]$, exactly the required $t$ distribution with one degree of freedom. The equivalent form $Z_1/|Z_2|$ has the same law by symmetry.