25. She was over the age limit and ________, her application for the job was rejected.
A. as a result B. in conclusion C. worse still D. what’s more
24. After five years of preparation, Shanghai is presenting the world _______ many say is the greatest Special Olympics.
A. when B. what C. where D. which
23. ---He suggests the number of cars should be limited to stop air pollution.
--- __________, the idea is not very practical.
A. Sounds good as it B. As it sounds good
C. As good it sounds D. Good as it sounds
22. Scientists are trying to develop a special material, _______ they will make use of in space.
A. it B. that C. what D. one
第一節:單項填空:(共15小題;每小題1分,滿分15分)
21. The education of _______young is always _______ hot and serious topic in modern society.
A. the; / B. a; the C. /; the D. the; a
4.已知非零實數a、b滿足,求
的值
解法一:所給等式左邊的分子、分母同除以a,則已知等式化為關于的方程,可求出
解:由題設得
解這個關于的方程得
解法二:已知等式的左邊的分子、分母都具有asinα+bcosα的結構,可考慮引入輔助角求解
解:∵
其中,即
∴由題設得
故,即
(k∈Z)
因此,
解法三:在已知等式的左邊,分子與分母同時除以acos得:
令=tanθ,則
∴
評注:解法一利用了集中變量的思想,是一種基本方法解法二通過模式聯想,引入輔助角,解法三通過聯想兩角和的正切公式,利用了換元法,實質上是綜合了解法一和解法二的優點
2.已知α、β、γ組成公差為的等差數列,求tanα·tanβ+tanβtanγ+tanγtanα的值
分析:條件的使用形式較多,可以把α、β、γ通過條件置換成β=α=,γ=α+
π;也可以用等差中項公式β=
,但兩種形式置換后的結果比較復雜
化切為弦雖是一種常用方法,但在這里效果不明顯
如果換個角度使用條件,即把條件變為β-α=
,γ-β=
,γ-α=
π,兩邊取正切后可分別出現所求式中的tanαtanβ、tanβtanγ、tanγtanα,然后將它們整體代入,便可使問題解決
解:由條件得β-α=,兩邊取正切得tan (β-α)=tan
,即
,化簡可得tanαtanβ=
(tanβ-tanα)-1
①
同理,由γ-β=得tanγtanβ=
(tanγ-tanβ)-1
②
由γ-α=π得tanγtanα=
(tanα-tanγ)-1
③
以上三式相加得tanαtanβ+tanβtanγ+tanγtanα=-3
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