If 2tanx+cotx=tan, prove that cotx=2tan(x-y).
Your question is incomplete as the first condition(2tax+cotx=tan)doesn't have a y term with the help of which you will require to prove the next part of the questions.
But to answer in general you can try and use formulas like tan(x-y)=tanx-tany/1+tanxtany. You can also express cot x as 1/tan x and solve further.