In Riley, Hobson & Bence's "Mathematical methods for physics and engineering" third edition, in the chapter about tensors, one of the exercises involves finding the expression for the divergence in spherical coordinates.
But when I looked in the solutions manual, it tells you that, for orthogonal systems, $g_{ij} = h_i\delta_{ij}$ and $g^{ij} = h_i^{-1}\delta_{ij}$ where $g_{ij}$ are the covariant components of the metric tensor and $h_i$ are the scale factors.
For the life of me, I can't find where these identities come from. Could someone help me with the derivation? It's not a homework question, I was just interested in deriving these equalities they use and am not able to. I haven't found them in the book.
Many thanks for your help!