已知函数f(x)=2sin(x+π/6)-2cox.(1)求函数f(x)的单调增区间,(2)若f(x)=6/5,求cos(2x-π/3)的值

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已知函数f(x)=2sin(x+π/6)-2cox.(1)求函数f(x)的单调增区间,(2)若f(x)=6/5,求cos(2x-π/3)的值
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已知函数f(x)=2sin(x+π/6)-2cox.(1)求函数f(x)的单调增区间,(2)若f(x)=6/5,求cos(2x-π/3)的值
已知函数f(x)=2sin(x+π/6)-2cox.(1)求函数f(x)的单调增区间,(2)若f(x)=6/5,求cos(2x-π/3)的值

已知函数f(x)=2sin(x+π/6)-2cox.(1)求函数f(x)的单调增区间,(2)若f(x)=6/5,求cos(2x-π/3)的值
(1)f(x)=2sin(x+π/6)-2cosx=3^(1/2)sinx-cosx=2sin(x-π/6)
所以,其实单调增区间应满足,2kπ-π/2≤x-π/6≤2kπ+π/2
求得2kπ-π/3≤x≤2kπ+2π/3
(2)f(x)=2sin(x-π/6)=6/5,则sin(x-π/6)=3/5
cos(2x-π/3)=cos2(x-π/6) =1-2sin^2[(x-π/6)]=1-2*(3/5)^2=1-18/25=7/25