题目

President John Kennedy was a reader and writer．President Lyndon Johnson was a listener．President Johnson didn’t do as well as he could in the White House because he thought he had to follow Kennedy’s way of learning and absorb everything through writing．As well written as those reports were, he couldn’t understand them as well as Kennedy．It wasn’t until many years after the White House that Johnson recognized what type of learner he was．Now, all we can do is think of the possibilities of how different the United States would be right now if he learned sooner． Eisenhower was已知a，b，c为△ABC的内角A，B，C的对边，满足，函数f（x）=sinωx（ω＞0）在区间上单调递增，在区间上单调递减．（Ⅰ）证明：b+c=2a；（Ⅱ）若，证明：△ABC为等边三角形．