Step 1: Set up the phenoxide.
Removing a proton from phenol gives the phenoxide ion, whose negative charge is shared between the oxygen and the ring.
Step 2: Behaviour in ether.
In a weakly interacting ether solvent the oxygen stays very nucleophilic, so alkylation lands on oxygen. That is O-alkylation, making statement A true.
Step 3: Behaviour in trifluoroethanol.
This solvent donates strong hydrogen bonds and ties up the oxygen, lowering its reactivity. Now the ring carbon takes over, so C-alkylation rises and statement B is true.
Step 4: Reject C and D.
Ethers have no acidic hydrogen, so they cannot hydrogen bond strongly to the phenoxide oxygen, making C false. C-alkylation happens at ortho or para while keeping the ring aromatic, so D is false too.
Step 5: Answer.
\[ \boxed{A,\ B} \]