I don't think it would make much sense to hunt large predators prior to the invention of agriculture, even though early humans were probably plenty smart enough to build traps capable of holding animals like tigers. But after that (less than 40k years ago, more than 10k years ago), I'd bet it was a common-ish thing for humans to try to hunt predators that preyed upon their livestock.

Tigers are terrifying, though. I think it takes extreme or perverse circumstances to make hunting a tiger make any sense at all. And even then, traps and poisons make more sense than stalking a tiger to kill it!