Formula for the autocorrelation function of torsions

GROMACS version: 2020
GROMACS modification: No

In the documentation for the gmx chi program, we are told that to solve the problem of periodicity in the angles, the autocorrelation functions of the torsions are calculated, i.e. C(t) = <cos(chi(tau)) cos(chi(tau+t))>. The relevant reference is Van der Spoel & Berendsen (1997), Biophys. J. 72, 2032-2041).
However, in that paper, Eq. 2 indicates that C(t) = <cos(chi(tau)) cos(chi(tau+t)) + sin(chi(tau)) sin(chi(tau+t))> should be used instead, as this has the advantage of having C(0)=1.

Which method was finally implemented? And in case the cosine-only form was used, why?