2kπ+π/2≤2x-π/6≤2kπ+3π/2时,函数单调递减
∴2kπ+2π/3≤2x≤2kπ+5π/3
∴kπ+π/3≤2≤kπ+5π/6
即单调件区间为[kπ+π/3,π+5π/6] k∈Z