I have seen the answer to this question - Great arc distance between two points on a unit sphere
However in a fortran program that I have this is the code to calculate spherical distance between two points - presuming lambda is longitude and theta is latitude
arg=$\sin\theta_1$ * $\sin\theta_2$ + $\cos\theta_1$ *$\cos\theta_2$ * $\cos(\lambda_1-\lambda_2)$
The identity referenced in the linked answer is given below. Can these be shown to be equivalent ?
$\cos\theta_1$ $\cos\theta_2$ + $\sin\theta_1$ $\sin\theta_2$ $\cos(\psi_1 - \psi_2)$