Complex sentence: The Grease Band was a British rock band that started out as Joe Cocker's backing band, appearing with Cocker in the 1960s, including his performance at the Woodstock Festival in August 1969.
Split into simpler sentences: The Grease Band was a British rock band that originally formed as Joe Cocker's backing group. They appeared with Cocker during the 1960s, including his performance at the Woodstock Festival in August 1969.