在△ABC中,∠A=120°
(Ⅰ)若三边长构成公差为4的等差数列,求△ABC的面积;
(Ⅱ)已知AD是△ABC的中线,若
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,求
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的最小值.
考点分析:
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设函数f(x)=sinx+cosx,g(x)=f(x)•f′(x)+[f(x)]
2(Ⅰ)求g(x)的周期和最大值;
(Ⅱ)求g(x)的单调递增区间.
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下列命题中,正确的是
①平面向量
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123936556475619/SYS201310251239365564756015_ST/0.png)
与
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123936556475619/SYS201310251239365564756015_ST/1.png)
的夹角为60°,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123936556475619/SYS201310251239365564756015_ST/2.png)
=(2,0),|
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123936556475619/SYS201310251239365564756015_ST/3.png)
|=1,则|
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123936556475619/SYS201310251239365564756015_ST/4.png)
|=
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123936556475619/SYS201310251239365564756015_ST/5.png)
;
②已知
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123936556475619/SYS201310251239365564756015_ST/6.png)
=(sinθ,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123936556475619/SYS201310251239365564756015_ST/7.png)
),
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123936556475619/SYS201310251239365564756015_ST/8.png)
=(1,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123936556475619/SYS201310251239365564756015_ST/9.png)
)其中θ∈(π,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123936556475619/SYS201310251239365564756015_ST/10.png)
)则
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123936556475619/SYS201310251239365564756015_ST/11.png)
;
③O是△ABC所在平面上一定点,动点P满足:
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123936556475619/SYS201310251239365564756015_ST/12.png)
+λ(
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123936556475619/SYS201310251239365564756015_ST/13.png)
+
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131025123936556475619/SYS201310251239365564756015_ST/14.png)
),λ∈(0,+∞),则直线AP一定通过△ABC的内心.
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