若三角形ABC三个内角A,B,C依次成等差数列,且U=cosA+2icos平方C/2,求|U-i|的取值范围

若三角形ABC三个内角A,B,C依次成等差数列,且U=cosA+2icos平方C/2,求|U-i|的取值范围
若三角形ABC三个内角A,B,C依次成等差数列,且U=cosA+2icos平方C/2,求|U-i|的取值范围

若三角形ABC三个内角A,B,C依次成等差数列,且U=cosA+2icos平方C/2,求|U-i|的取值范围
由已知,设A=B-α,C=B+α,则A+B+C=3B=π
所以：B =π/3
U=cosA+2icos²(C/2)
=cosA+i(1+cosC)
=cosA+i+icosC

|U-i|=|cosA+icosC|
=√(cos²A+cos²C)
=√(2+cos2A+cos2C)/2
=√[1+cos(A+C)cos(A-C)]
=√[1+cos(2π/3)cos(A-C)]
=√[1-(cos2α)/2]
显然-π/3＜α＜π/3,-1/2＜cos2α≤1
1/2≤1-(cos2α)/2＜5/4
√2/2≤|U-i|＜√5/2

How to Ablution an Authentic NFL Jersey
You accept gotten your easily on an NFL jersey. Not a kids' version, not a replica, but the absolute thing. You couldn't be prouder and of advance you abras...

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How to Ablution an Authentic NFL Jersey
You accept gotten your easily on an NFL jersey. Not a kids' version, not a replica, but the absolute thing. You couldn't be prouder and of advance you abrasion it every Sunday back your aggregation plays a game. You abrasion it all day and at the end of the day you may accept sweated as abundant as your admired players. You charge to apple-pie your admired jersey and you appetite it to arise out in as acceptable a appearance as you got it.
Step 1
Hand ablution your jersey. It is recommended by NFL accessories managers to use a non-abrasive, color-fast bactericide to ablution jerseys. Woolite matches this description. Run air-conditioned baptize in a ample sink, cascade one cap of Woolite into the active baptize and suds will appear. Put the jersey in and authentic nfl jerseys ablution immediately.
Step 2
Rinse the jersey thoroughly by elimination the bore and accepting rid of the suds. Then put the jersey in active algid baptize and get all of the bactericide out of it. Check your jersey already the soap is out and it is rinsed; it should be apple-pie and it should accept a actual affable and beginning smell.
Step 3
Wash the jersey afresh in the color-fast bactericide if all the stains accept not arise out. A additional abrasion will abolish all stains except annihilation permanent. It will booty out blood. After abrasion it a additional time, bathe thoroughly.
Step 4
Line dry your NFL jersey. The worse aberration you can accomplish is to put it in the dryer. Putting it in the dryer will accident the numbers, belletrist and symbols on the uniform. Let it band dry for about 24 hours in a non-humid area.
Step 5
Take your jersey to the dry cleaner if you are not accomplished at hand-washing it. The dry cleaner uses chemicals and not calefaction drying, so your jersey authentic mlb jerseys will be safe.
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