tanx的增区间为 (kπ-π/2,kπ+π/2)
则tan(x/2-π/6)的单调增区间 是
kπ+π/2>x/2-π/6>kπ-π/2
kπ+2π/3 = kπ+π/2+π/6 >x/2>kπ-π/2+π/6=kπ-π/3
2kπ+4π/3>x>2kπ-2π/3
所以
函数y=tan(x/2-π/6)的单调增区间 是(2kπ-2π/3 ,2kπ+4π/3)