题目

已知cosa＝，cos（a－b）＝，且0＜b＜a＜． （1）求tan2a的值； （2）求角b的值． 答案：(Ⅰ)  －  (Ⅱ) b＝ 解析:（1）由cosa＝，0＜a＜，得sina＝．所以tana＝＝4 tan2a＝＝－． （2）由0＜b＜a＜得0＜a－b＜，又cos（a－b）＝，所以sin（a－b）＝．cosb＝cos［a－（a－b）］＝cosacos（a－b）＋sinasin（a－b）＝×＋×＝，所以b＝．There was great excitement on the planet of Venus (金星). Venusian scientists managed to land a satellite on the planet Earth, and it has been sending back signals as well as photographs ever since. The satellite was directed into an area known as Manhattan, named after the great Venusian astronomer Professor. Manhattan, who first discovered it with his telescope 20000 light years ago.Because of excellent weather conditions and extremely strong signals, Venusian scientists were able to get valuable information as to feasibility (可行性) of a manned flying saucer landing on Earth. A press conference was held at the Venus Institute of Technology. “We have come to the conclusion, based on last week's satellite landing，” Prof. Zog said, “that there is no life on Earth.” “How do you know this？” the science reporter of the Venus Evening Star asked. “For one thing, Earth's surface in the area of Manhattan is made up of solid concrete and nothing can grow there. For another, the atmosphere is filled with carbon monoxide (一氧化碳) and other deadly gases and nobody could possibly breathe this air and survive.” “What does this mean as far as our flying saucer program is concerned？” “We shall have to take our own oxygen with us, which means a much heavier flying saucer than originally planned.” “Are there any other dangers that you discovered in your studies？” “Take a look at this photo. You see this dark black cloud hovering (盘旋) over the surface of Earth? We don't know what it is made of, but it could give us a lot of trouble and we shall have further tests before we send a Venus Being there.”“Over here you will notice what seems to be a river, but the satellite findings indicates it is polluted and the water is unfit to drink. This means we shall have to carry our own water, which will add even greater weight to the saucer.” “If all you say is true, won't this set back the flying saucer program several years？” “Yes, but we shall continue as soon as the Grubstart gives us the added funds(资金)．” Profession. Zog replied. 1.According to the passage, the Venusian scientists succeeded in getting important information about ________.A．the feasibility of landing a satellite on Earth B．the possibility of making a first­rate flying saucerC．the feasibility of sending a Venus Being to Earth D．the possibility of directing a flying saucer into Manhattan2.Why will the Venusian have to take their own oxygen with them when they carry out their flying saucer program because ________.A．they need it in their way to the planet of EarthB．the Earth's atmosphere is filled with deadly gases C．there is a low level of oxygen for Venusians D．there is no air on the planet of Earth 3.It can be inferred from the passage that ________. A．landing a manned flying saucer on Earth will be carried out soonB．Venusians will land on Earth to help to stop serious pollutionC．it's unnecessary to land a manned flying saucer on Earth at presentD．pollution on Earth makes it impossible for Venusians to survive there4.Where can you probably read such a passage?A．In a popular magazine.B．In a fairy tale.C．In an observation journalD．In science fiction