已知 $0<\beta <\alpha <\frac{\pi }{2}$ ，且 $\cos \alpha =\frac{5}{13}$ ， $\cos \left(\alpha -\beta \right)=\frac{4}{5}$ ．

（Ⅰ）求 $\cos (\alpha +\frac{\pi }{4})$ 的值；

（Ⅱ）求sin（α﹣β）的值．

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    When Jeanne Calment entered the world in 1875, telephones and automobiles still lay in the future. Albert Einstein and Pablo Picasso were not yet born. The Eiffel Tower was 14 years from being built. As a teenager, she met Vincent Van Gogh, near her home in Arles, in the south of France. He was “very ugly, ungracious, impolite, sick—I forgive him, they called him loco (精神失常的)”, she recalled. When she died last week at age 122, she was the world's eldest person. (There are others who claimed to the title, but only Calment had the official documents to prove her age.)

    Each February 21, her birthday, she would share the secrets of long life. Some years it was “a sense of humour”, others it was “keeping busy”. “God must have forgotten me,” she once explained. The truth probably was that her mother reportedly lived to be 86 and her father 94.

    Her life had its sadness: she outlived her husband, her only daughter and her grandson. According to a friend, she was imperturbable. “If you can't do anything about it,” she reportedly said, “don't worry about it.”

    In her last years she was nearly blind and deaf, but her health remained good. She ate a few bars of chocolate each week and continued smoking until a few years ago, when she could no longer light her own cigarettes. She never lost her sense of humour. On her 110^th birthday, she commented, “I've only ever had one wrinkle, and I'm sitting on it. “Her longevity made her famous; her spirit made her eternal (永恒的).