For some reason this scene was cut before the theatrical release. It’s in the director’s-cut DVD though.
FADE IN: EXT. ELVEN FOREST - DAY (SAM, FRODO, GOLLUM) SAM AND FRODO SLUMP AGAINST A LOG. GOLLUM COWERS A FEW FEET AWAY. BIRDS TWITTER. SAM LOOKS AT FRODO. SAM Guess we can rest here for a time, Mister Frodo. FRODO Yes, Sam. SILENCE. GOLLUM SCRATCHES ON THE GROUND WITH HIS FINGERNAILS. SAM COUGHS. FRODO (CONT'D) Did you say something? SAM No. FRODO What? SAM I just coughed. GOLLUM Hobbitzes always coughingzess! Nasty sounds he makes! SAM Shut up, you! FRODO SIGHS. LONG SILENCE. SAM COUGHS. FRODO Um... SAM Yes? FRODO Nothing. SAM No, what? FRODO Nothing. Really, Sam. LONG SILENCE. GOLLUM (coughs) Gollum! Gollum! FRODO SIGHS AND CLOSES HIS EYES.