题目

已知下列四个命题：①若tan θ＝2，则sin 2θ＝；②函数f(x)＝lg(x＋)是奇函数；③“a>b”是“2a>2b”的充分不必要条件；④在△ABC中，若sin Acos B＝sin C，则△ABC是直角三角形．其中所有真命题的序号是________． 答案：【答案】①②④【解析】①中，利用三角函数的基本关系，即可得到，所以是真命题；②中，根据函数的奇偶性和对数的运算，得到是真命题；③根据指数函数的单调性，可判定为假命题；④中利用两角和的正弦函数公式，可得，可得是真命题.因为，则，故①是真命题；函数的定义域为，且，故是奇函Lots of students shop to reduce stress or just to kill time with their friends．Shopping to get rid of boredom or to escape from life’s pressures may lead to serious problems．When you start to shop out of control, you become a shopping addict．        Shopping addicts show signs that are similar to other addicts．Some students think that shopping, even as little as buying gifts for classmates, can make them feel better and forget their problems．Actually, it can make them feel worse, guilty, or even cause them to run into financial difficulties．Finding yourself in a financial struggle or deep in debt may harm your relationships with friends and parents．        Do you go shopping for just a few things and come home with your wallet empty? Do you always go shopping after an emotional trauma or when life feels tough（艰难的）? Do you regret later what you buy? Or do you buy things that you never use? Maybe your parents or friends have expressed disagreement that leads you to hide items or lie about prices．        Avoid any environment that may make you want to spend money．Never use credit cards．Form some other meaningful and beneficial hobbies．Exercise, yoga and hot baths generally may help you not want to shop．Take a drive through the country where there aren’t any stores．Have patience with yourself and your money, which can benefit you for the rest of your life． 1．According to the passage, shopping addicts ______．        A．are always rich people                B．get well along with friends        C．may suffer financial difficulties         D．all the above 2．The third paragraph mainly tells about ______．        A．ways to get rid of shopping addiction        B．the signs of shopping addicts        C．the danger of shopping addiction        D．why shopping addicts can’t stop shopping 3．The underlined word “trauma” probably means “______”．        A．hurt               B．satisfaction         C．enjoyment        D．appreciation 4．The intended readers of the passage are ______．        A．teachers        B．doctors          C．students         D．education