题目内容
若![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202111408023003015/SYS201312021114080230030009_ST/0.png)
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202111408023003015/SYS201312021114080230030009_ST/1.png)
A.
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202111408023003015/SYS201312021114080230030009_ST/2.png)
B.-2sin
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202111408023003015/SYS201312021114080230030009_ST/3.png)
C.2cos
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202111408023003015/SYS201312021114080230030009_ST/4.png)
D.-2cos
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202111408023003015/SYS201312021114080230030009_ST/5.png)
【答案】分析:利用二倍角公式,结合θ的范围,化简表达式的值,求出交点范围,然后求出表达式的值.
解答:解:![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202111408023003015/SYS201312021114080230030009_DA/0.png)
=![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202111408023003015/SYS201312021114080230030009_DA/1.png)
=|
|+|
|.
因为
,所以
.
,
所以|
|+|
|
=![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202111408023003015/SYS201312021114080230030009_DA/9.png)
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202111408023003015/SYS201312021114080230030009_DA/10.png)
=-2cos
.
故选D.
点评:本题是中档题,考查三角函数的化简求值,注意角的范围与三角函数的符号,考查计算能力.
解答:解:
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202111408023003015/SYS201312021114080230030009_DA/0.png)
=
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202111408023003015/SYS201312021114080230030009_DA/1.png)
=|
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202111408023003015/SYS201312021114080230030009_DA/2.png)
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202111408023003015/SYS201312021114080230030009_DA/3.png)
因为
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202111408023003015/SYS201312021114080230030009_DA/4.png)
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202111408023003015/SYS201312021114080230030009_DA/5.png)
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202111408023003015/SYS201312021114080230030009_DA/6.png)
所以|
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202111408023003015/SYS201312021114080230030009_DA/7.png)
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202111408023003015/SYS201312021114080230030009_DA/8.png)
=
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202111408023003015/SYS201312021114080230030009_DA/9.png)
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202111408023003015/SYS201312021114080230030009_DA/10.png)
=-2cos
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202111408023003015/SYS201312021114080230030009_DA/11.png)
故选D.
点评:本题是中档题,考查三角函数的化简求值,注意角的范围与三角函数的符号,考查计算能力.
![](http://thumb.zyjl.cn/images/loading.gif)
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