Nurse Mary Louise Wallace left the Alpine Inn at Crows Nest in September 1983 with Robert John Adams, who had offered to give her a lift home.
She was never seen again.
At the time, Adams told police he had sexual contact with Ms Wallace in his car but then fell asleep and when he woke, she was gone.
Prosecutors will call evidence from three women, who have told police Adams raped and attempted to choke them, in the 1970s.
Adams served two years of a six-year sentence for one of the incidents.
One woman said she fled Sydney before Adams went on trial over the attack on her in 1975, because she feared for her life.
Another woman told two friends at the time that she had been raped.
The murder case was reopened by the Unsolved Homicide Team in 2008 and was the subject of a coronial inquest in 2010.
In 2013, Adams was arrested and charged with murder.
It was 30 years since Ms Wallace had disappeared, at the age of 33.
Adams’ trial is being held without a jury in the NSW Supreme Court.
Adams became a suspect early in the investigation, police say
His then flatmate, Suzanne Beckingham, told police she saw Adams clean his car outside their Chatswood unit on September 25, 1983.
This was the day after Ms Wallace’s disappearance.
She said she saw Adams fetch a vacuum cleaner from inside and return with it 20 minutes later.
Prosecutor Mark Hobart SC said Adams “emptied everything from the boot of his vehicle, including the carpet”.
“[Ms] Beckingham had never seen him do this before,” Mr Hobart said.
Adams’ car was scientifically examined within a fortnight of Ms Wallace’s disappearance.
Police also seized the contents of the vacuum cleaner.
The samples were later re-examined, due to advancements in technology.
Two hairs which had been vacuumed from the boot, were found to found to be identical to samples from Ms Wallace’s hairbrush, when viewed under a microscope.
The samples were also subjected to DNA testing.
“These were examined and no differences were detected between the mitochondrial DNA profiles of the two hairs from the boot of the accused’s vehicle and the hair taken from the hairbrush seized from Ms Wallace’s apartment,” Mr Hobart said.
Mary Williams, who worked with Ms Wallace at Hunters Hill Private Hospital, said Adams had broken down the door of a toilet cubicle at the Alpine Inn because she had gone to check on Ms Wallace and she was not responding.
Ms Williams then helped Ms Wallace to Adams’ car and she was placed into the front passenger seat.
They were then seen driving along Willoughby Road towards Willoughby.
The lengthy police investigation has included searches of a number of bushland areas in Sydney but Ms Wallace’s body has never been found.