Also, in the deposition, the now-79-year-old said he gave the medication to a woman named "Teresa", and promised to tell Constand's mother what pills he gave her daughter but later changed his mind in fear that their conversation would be recorded.
"I didn't know where she was going with her questions and I - from her tone - felt like I was being attacked", he said.
Prosecutors plan to close their case Friday afternoon after five days of testimony. Pacing the floor, the lawyer showed the courtroom a Facebook post from Valliere's company linking to a Washington Post article about the Cosby case during the pretrial period.
McMonagle, sounding highly irritated, pointed to continued objections to Valliere's testimony, and said the woman's testimony has essentially instructed jurors on what their eventual verdict should be.
Sections of the deposition were unsealed two years ago in a different legal proceeding and became a driving force behind prosecutors' decision to charge Cosby with three counts of aggravated indecent assault on December 2015.
Montgomery County Det. James Reape read aloud from the deposition Cosby provided to authorities in 2005 in court on Friday.
Another detail revealed in the now-public deposition was that Cosby apologized to Constand's mother, though not, he says, for any kind of assault.
The prosecution rested their case Friday, which means the trial will be turned over to Cosby's defense attorney - who still isn't ruling out the possibility that their client might testify.
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According to the deposition, Cosby admitted to giving Quaaludes to multiple women before sex.
Prosecutors on Friday are expected to continue presenting jurors with portions of Cosby's deposition, including his admission that he gave the sedative Quaalude to young women.
"It had more to do with business than it did with me personally", she said.
"I apologized to this woman".
Defense attorney Brian McMonagle said no one asked Cosby to bring the pills to the 2005 interview, he voluntarily provided pills and that he had no obligation to talk to anyone.
Andrea Constand is accusing Cosby of drugging her and sexually abusing her as she drifted in and out of consciousness. Cosby has said the encounter was consensual. The Philadelphia trial is the only criminal case against Cosby.
In a barrage that all but destroyed Cosby's good-guy reputation, some 60 women have come forward to say he sexually violated them, but the statute of limitations for prosecution had run out in almost every case. Constand refused the offer and reported Cosby to police, suing him after prosecutors failed to file charges. After "necking" on the couch, Cosby went to bed and Constand slept on the couch.
Constand testified this week that Cosby gave her pills that made her woozy, then violated her. Cosby has said he gave Constand the cold and allergy medicine Benadryl to help her relax, but prosecutors have suggested he drugged her with something stronger.
Cosby at courthouse with "Cosby Show" co-star Keshia Knight-Pulliam.