Do the joints in adjustable duct elbows need to be taped as well once they're adjusted or are they considered air-tight?
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Do the joints in adjustable duct elbows need to be taped as well once they're adjusted
Yes, they do.
or are they considered air-tight?
No, they are not. Far from it, in fact.
You want to tape every seam in your ductwork, using (as Shirlock pointed out) foil tape. Each exposed seam, whether it's at a connection or part of pre-formed metal like the elbow in question, is a leak point.
Do NOT use Duct or Duck tape as the backing for it degrades over time, faster with heat.
Edit: Even though this is for a bathroom fan, you still want to tape. Why? Because air leakage is moisture leakage, and you do not want to be pumping moisture into your attic. In winter it will lead to frost which will lead to mold.