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问题 解答题
已知下列命题：
（1）θ是第二象限角；
（2）sin
θ
2
+cos
θ
2
=-
7
5
；
（3）tan
θ
2
=
4
3
；
（4）tan
θ
2
=
3
4
；
（5）sin
θ
2
-cos
θ
2
=-
1
5

试以其中若干（一个或多个）命题为条件，然后以剩余命题中的若干命题为结论，组成新命题，并证明之．
答案

以（1）（2）为条件，以（3）为结论．

证明：因为θ是第二象限角，

所以kπ+

π
4
＜
θ
2
＜kπ+
π
2
，k∈Z．①

又sin

θ
2
+cos
θ
2
=-
7
5
，

所以2kπ+π＜

θ
2
＜2kπ+
3
2
π，k∈Z．②

由①②可知2kπ+

5
4
π＜
θ
2
＜2kπ+
3
2
π．

又由sin

θ
2
+cos
θ
2
=-
7
5
，得sin
θ
2
•cos
θ
2
=
12
25
，

所以

sin
θ
2
•cos
θ
2
sin2
θ
2
+cos2
θ
2
=
12
25
．分子分母同除以sin
θ
2
•cos
θ
2
可化得，

所以12tan2

θ
2
-25tan
θ
2
+12=0．

解得tan

θ
2
=
3
4
（舍），或tan
θ
2
=
4
3
．

∴tan

θ
2
=
4
3
．

单项选择题

Every group has a culture, however uncivilized it may seem to us. To the professional anthropologist, there is no intrinsic superiority of one culture over another, just as to the professional linguist, there is no intrinsic hierarchy among languages.
People once thought of the languages of backward groups as undeveloped. While it is possible that language in general began as a series of grunts and groans, it is a fact established by the study of "backward" languages that no spoken tongue answers that description today. Most languages of uncivilized groups are, by our most severe standards, extremely complex. They differ from Western languages not in their sound patterns or grammatical structures, which usually are fully adequate for all language needs, but only in their vocabularies, which reflect the objects and activities known to their speakers. Even in this aspect, two things are to be noted. First, all languages seem to possess the machinery for vocabulary expansion, either by putting together words already in existence or by borrowing them from other languages and adapting them to their own system. Second, the objects and activities requiring names and distinctions in "backward" languages, while different from the West, are often surprisingly numerous and complicated. A Western language distinguishes merely between two degrees of remoteness ("this" and "that"). But some languages of the American Indians distinguish between what is close to the speaker, or to the person addressed, or removed from both, or out of sight, or in the past, or in the future.

This passage is on the whole______.

A．narrative

B．instructive

C．prescriptive

D．argumentative
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判断题

贷记卡是指持卡人须先按发卡银行的要求交存一定金额的备用金。
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