∵tanα=3tanβ，又0≤β＜α＜π2，∴tanβ＞0，∴tan（α-β）=tanα−tanβ1+tanαtanβ=2tanβ1+3tan2β=21tanβ+3tanβ．∵tanβ＞0，∴3tanβ+1tanβ≥23，∴0＜21tanβ+3tanβ≤223=33，∴0＜tan（α-β）≤3...