题目

John graduated from a key university and he was very good at his major. He wished to find a good job. One day, he went to a company to   21   for a job. He got the news in a newspaper. He did some research on this company. When he was    22  , everything went well. The manager asked him some questions and he answered them   23  . John was very satisfied with his performances and was very   24   that he could get the job. But at that moment, the manager’s phone   25  . He picked up the phone, listened and nodded. And then he turned around and said to John, “Sorry9．已知cos（$\frac{π}{4}$-α）=$\frac{3}{5}$，sin（$\frac{π}{4}$+β）=$\frac{12}{13}$，α∈（$\frac{π}{4}$，$\frac{3π}{4}$），β∈（0，$\frac{π}{4}$），求sin（α+β）的值．