Projecting strength, control and power, whether as a New York developer or domineering reality television host, has always been vital to Mr. Trump. But in his first year in the White House, according to his friends, he found himself feeling tentative and anxious, intimidated by the role of president, a fact that he never openly admitted but that they could sense, people close to the president said…

They say Mr. Trump now feels he doesn’t need the expertise of Mr. Kelly, Mr. Cohn or Rex W. Tillerson, the former Exxon Mobil executive he made secretary of state. If he once suspected they were smarter or better equipped to lead the country and protect his presidency, he doesn’t believe that now…

“He seems more relaxed, believe it or not,” said Representative Peter T. King, a New York Republican who spent several hours with the president during two St. Patrick’s Day events on Thursday.