∵y=tan(-x-π/6)=-tan(x+π/6)
由kπ-π/2<x+π/6<kπ+π/2,(k是整数)
→ kπ-2π/3<x<kπ+π/3(k是整数)
∴y=tan(-x-π/6)的单调递减区间是(kπ-2π/3,kπ+π/3)(k是整数).
∵y=tan(-x-π/6)=-tan(x+π/6)
由kπ-π/2<x+π/6<kπ+π/2,(k是整数)
→ kπ-2π/3<x<kπ+π/3(k是整数)
∴y=tan(-x-π/6)的单调递减区间是(kπ-2π/3,kπ+π/3)(k是整数).