设函数f(x)=2cosxsin(x+派/6)+2sinxcos(x+派/6) 当x属于[0,派]时.求
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设函数f(x)=2cosxsin(x+派/6)+2sinxcos(x+派/6) 当x属于[0,派]时.求f(x)的值域
麻烦
麻烦
![设函数f(x)=2cosxsin(x+派/6)+2sinxcos(x+派/6) 当x属于[0,派]时.求](/uploads/image/z/19443969-9-9.jpg?t=%E8%AE%BE%E5%87%BD%E6%95%B0f%28x%29%3D2cosxsin%28x%2B%E6%B4%BE%26%2347%3B6%29%2B2sinxcos%28x%2B%E6%B4%BE%26%2347%3B6%29+%E5%BD%93x%E5%B1%9E%E4%BA%8E%5B0%2C%E6%B4%BE%5D%E6%97%B6.%E6%B1%82)
f(x)=2cosxsin(x+派/6)+2sinxcos(x+派/6)
=2cosxsin(x+π/6)+2sinxcos(x+π/6)
=2sin(x+π/6+x)
=2sin(2x+π/6)
0≤x≤π→0≤2x≤2π→π/6≤2x+π/6≤2π+π/6→-2≤2sin(2x+π/6)≤2
f(x)的值域[-2,2]
=2cosxsin(x+π/6)+2sinxcos(x+π/6)
=2sin(x+π/6+x)
=2sin(2x+π/6)
0≤x≤π→0≤2x≤2π→π/6≤2x+π/6≤2π+π/6→-2≤2sin(2x+π/6)≤2
f(x)的值域[-2,2]
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