I just recorded a solo sitar piece yesterday in a live room. I used two mics:
Schoeps MK62 (omni) about 2 feet from the instrument aimed at the "gourd" slightly to the left of the bridge and above it. The sweet spot with the omni is very precise.
Schoeps MK641 (hypercard) about four feet away and three feet up pointed slightly downwards. Recording is still quite bright but bringing the mic closer makes it base heavy due to the proximity effect of the hypercard capsule.
This player's instrument had a bright tone to begin with so the Omni worked best. At other times, the hypercard has given the better result. Also, if the instrument has a base string (some do, some don't) the omni is the way to go.
Recording a tanpura ... that is a whole another topic.
Hope this helps,