已知向量a=(2,cosx),向量b=(sin(x+π/6),-2),f(x)=向量a*向量b（x属于R）.求函数f(x)单调增区间；若f(x)=6/5,求cos(2x-π/3的值

已知向量a=(2,cosx),向量b=(sin(x+π/6),-2),f(x)=向量a*向量b（x属于R）.求函数f(x)单调增区间；若f(x)=6/5,求cos(2x-π/3的值
已知向量a=(2,cosx),向量b=(sin(x+π/6),-2),f(x)=向量a*向量b（x属于R）.
求函数f(x)单调增区间；若f(x)=6/5,求cos(2x-π/3的值

已知向量a=(2,cosx),向量b=(sin(x+π/6),-2),f(x)=向量a*向量b（x属于R）.求函数f(x)单调增区间；若f(x)=6/5,求cos(2x-π/3的值
f(x)=2sin(x+π/6)-2cosx和角公式展开,化简得：
f(x)=√3sinx-cosx=2sin(x-π/6)
x-π/6∈[－π/2+2kπ,π/2+2kπ]
解出x即是增区间.
2sin(x-π/6)＝6/5
sin(x-π/6)＝3/5
cos(2x-π/3)=1-2sin(x-π/6)^2=7/25