Trivedi has composed the title track of Bachchan's upcoming TV show "Aaj Ki Raat Hai Zindagi".
"Bachchan saab (Amitabh Bachchan) is a very shy person. He said 'I'll not sing in front of you'. He feels very shy while signing in front of people. But then he found his confront zone and everything was smooth. It was fantastic recording the track," Trivedi told PTI.
The show, which marks the return of the 73-year-old "Piku" actor to small screen as a host, revolves around common people who have accomplished something extraordinary in their life.
"He is singing as well as narrating in the song. It has the signature baritone of Bachchan. When he was recording, my studio speakers were the happiest," Trivedi said.
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The "Shaandaar" composer was approached by Bachchan, who was keen to have him compose for the show.
"Bachchan saab called me directly. He wanted to meet me. So I visited him where he narrated me the story and gave me a brief of the show.
"So I'll say the song is jointly created by us. He has collaborated with me. It's Bachchan saab's idea, his plan and my execution," he added.
"The whole process has been great. It is a once in a lifetime opportunity to work with a stalwart like him. I am going to cherish this for my lifetime because the experience has been fantastic."
The series, an adaptation of British show "Tonight's the Night", aims to inspire people to change their outlook and cherish the good that life has to offer.
"Aaj Ki Raat Hai Zindagi" premieres on October 18 on Star Plus.