题目内容
函数y=tan ωx(ω>0)与直线y=a相交于A、B两点,且|AB|最小值为π,则函数f(x)=
sin ωx-cos ωx的单调增区间是________.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824040313883344.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824040313914915.png)
由函数y=tan ωx(ω>0)图象可知,函数的最小正周期为π,则ω=1,
故f(x)=
sin ωx-cos ωx=2sin
的单调增区间满足:
2kπ-
≤x-
≤2kπ+
(k∈Z)⇒2kπ-
≤x≤2kπ+
(k∈Z).
故f(x)=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824040313883344.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824040313945734.png)
2kπ-
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824040313961421.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824040313976420.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824040313961421.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824040314007413.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824040314023491.png)
![](http://thumb.zyjl.cn/images/loading.gif)
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