The dollar eased against a basket of currencies on Tuesday, trimming some of the previous day’s sharp gains as investor selling of stretched higher-yielding currencies and the euro paused. The euro had its steepest drop since early August on Monday, falling nearly 1 percent, and the dollar index posted its best daily gain since September as investors unwound short dollar positions after a sharp fall in stocks and commodities. The euro drew some demand from Asian investors, recovering from the day’s lows, while the Aussie rebounded as some market players remained doubtful that the low-yielding dollar would strengthen further. But other traders said the dollar may rise more in the near term as short-term speculators take profits from their bets this year on risky assets with the approach of their business year-end, which typically comes in November.