题目

已知锐角α，β满足：sinβ=2cos(α+β)sinα，记y=tanβ，x=tanα，    (Ⅰ)求y关于x的函数解析式y=f(x)及定义域；    (Ⅱ)求(Ⅰ)中函数y=f(x)的最大值及此时α，β的值. 答案：答案：解：(Ⅰ)∵sinβ=2cos(α+β)sinα，∴sin[(α+β)-α]=2cos(α+β)sinα，即sin(α+β)cosα=3cos(α+β)sinα  ①∵α，β都是锐角，∴0＜α+β＜π，sinβ＞sinα＞0，∴由sinβ=2cos(α+β)sinα知cos(α+β)＞0∴由①式，得tan(α+β)=3tanα，即=3tanα，即=3x∴y=(x＞0)，即所求函数的解析式为y=f(x)=，其定义域为(0，+∞)；(Ⅱ)由(Ⅰ)得，y==Ⅲ.短文填空根据短文内容及所给首字母?填写所缺单词，每空格填一词。        A thousand years ago,Hong Kong was cl by a thick forest. As more and more people came to live in Hong Kong,these trees were c 2 down and burnt. Now there is no forest left,though there are still some small areas covered with trees. We call these “woods”.        Elephants,tigers and many o 3 animals were living in the thick forest. When people came to live in Hong Kong ? the animals began to die out. Early farmers grew rice and r 4 pigs and chickens in the valleys. They cut down the trees and burnt them. They needed fire to keep t 5 warm in winter,to cook their food and to drive away the dangerous animals. Elephants quickly d 6 because there was not enough food for them. So did most of the wolves and tigers.        You might think that there are no longer any animals in Hong Kong e 7 in the zoos,but there are still about 36 different animals living there. One of the most lovely of Hong Kong ’ s animals is the barking deer. There are beautiful little animals w 8 a rich brown coat and a white patch under the tail. They look like deer but they are much smaller. They are less than two feet high. They make a noise rather like a dog barking. In Hong Kong the barking deer has only one r 9 enemy (敌人) 一men. People hunt these little animals though it is illegal (犯法的) .There are now not many barking deer 1 10 So it is important for people to protect these wild animals.1.   2.  3.  4.  5. 6.  7. 8.  9. 10.