It’s a case of dueling identities during Providence Performing Arts Center’s limited engagement of “Jekyll & Hyde.” Based on Robert Louis Stevenson’s novella, “The Strange Case of Dr. Jekyll and Mr. Hyde,” the story follows a London doctor who accidentally unleashes his evil, alternate personality during a quest to cure his father’s mental illness. Tony-Award nominee Constantine Maroulis will play the dual role of Dr. Henry Jekyll and Edward Hyde, alongside Deborah Cox, a Grammy-Award nominee and R&B singer, who will play Lucy.