Eddie Applegate, an actor best known for playing Patty Lane’s steadfast high school sweetheart on the 1960s sitcom “The Patty Duke Show,” died on Monday in Los Angeles. He was 81. His death was confirmed by his son Michael, who said Mr. Applegate had been living in a care facility after a stroke in 2013. Mr. Applegate was the third cast member from the show to die this year. Ms. Duke died in March, and William Schallert, who played her father, died in May. On the show, which ran on ABC from 1963 to 1966, Ms. Duke played identical cousins,...