f(x)=2sin(x/4)cos(x/4)-2根号3*sin²(x/4)+根号3 求1.当x∈[0,π],求f(x)值域2.f(x)单调递增区间

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f(x)=2sin(x/4)cos(x/4)-2根号3*sin²(x/4)+根号3 求1.当x∈[0,π],求f(x)值域2.f(x)单调递增区间
f(x)=2sin(x/4)cos(x/4)-2根号3*sin²(x/4)+根号3 求1.当x∈[0,π],求f(x)值域2.f(x)单调递增区间

f(x)=2sin(x/4)cos(x/4)-2根号3*sin²(x/4)+根号3 求1.当x∈[0,π],求f(x)值域2.f(x)单调递增区间
f(x)=2sin(x/4)cos(x/4)-2v3*sin²(x/4)+v3 
     =sin(x/2)-v3*(1-cos(x/2))+v3
      =sin(x/2)+v3cos(x/2)
      =2sin(x/2 +π/3)
x∈[0,π].      π/3=<x/2+π/3<=5π/6.根据图像值域为[1,2]
当π/3=<x/2+π/3<=π/2,f(x)递增,即x∈[0,π/3]


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