已知函数f(x)=asin(x-π/3)+asin(x+π/3)-2sin²x,其中x∈[0,π],a为常数.(1)求当sin(x-π/3)=1/2时,y=f(x)的值

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已知函数f(x)=asin(x-π/3)+asin(x+π/3)-2sin²x,其中x∈[0,π],a为常数.(1)求当sin(x-π/3)=1/2时,y=f(x)的值
已知函数f(x)=asin(x-π/3)+asin(x+π/3)-2sin²x,其中x∈[0,π],a为常数.
(1)求当sin(x-π/3)=1/2时,y=f(x)的值

已知函数f(x)=asin(x-π/3)+asin(x+π/3)-2sin²x,其中x∈[0,π],a为常数.(1)求当sin(x-π/3)=1/2时,y=f(x)的值
x∈[0,π]
-π/3≤x-π/3≤2π/3
sin(x-π/3)=1/2,
x=π/6,
f(π/6)=asin(π/6-π/3)+asin(π/6+π/3)-2sin²(π/6)
=-1/2 a+a-1/2
=(a-1)/2.