You need to be careful here: there are several similarly named species in English, so it's probably better to use the scientific name.
Fork-tailed drongo (Dicrurus adsimilis, e.g. this shot on ebird) is an African species that looks very much like your photo. India's black drongo (Dicrurus macrocercus) is a closely related species, formerly regarded as a subspecies of fork-tailed drongo (so if you've got an old book it might be listed under that name). The hint of brown on the wings is good, as is the red/brown in the eye.
Fork-tailed drongo-cuckoo (Surniculus dicruroides) is another Indian species, recently split from square-tailed drongo-cuckoo. It closely resembles the black drongo. While the iridescence is striking in the photo I've linked, ebird has a photo in a similar pose to yours (you'll have to go through the images; they don't make it easy to link directly) that isn't catching the light. Black drongo can also show iridescence.
Sound will be the best way to tell black drongo from fork-tailed drongo-cuckoo. These links are to recordings of both from Kerala (as some species have regional accents). Ebird has plenty of recordings of both. Ebird also states that the adult fork-tailed drongo-cuckoos "may be confused with drongos, but are lighter-billed and smaller, with distinctly white-barred undertail". The latter is pictured, but you'd need a good view to see it; as for the overall size and subtleties of the bill shape, familiarity with one species might indicate something off about a sighting, but in isolation they're not diagnostic.
In the photos I've seen, there's much more noticeable white on the lores (near the base of the bill) in the black drongo. Your photo shows a small patch. Combined with the eye colour I'm leaning towards black drongo. The bill shape is also good for black drongo, less curved than in the drongo-cuckoo (thanks to Tom Gaskill for pointing that out).