NEW YORK (Reuters) -Chip design software maker Synopsys said on Tuesday it would buy Ansys in a $35 billion cash-and-stock deal, snapping up the maker of software used in creating products from airplanes to tennis rackets of players like Novak Djokovic. The transaction would be the biggest acquisition in the technology sector since chipmaker Broadcom took over software maker VMware last November in a $69 billion deal. It could herald more big deals as a pick up in economic sentiment and some failed attempts by antitrust regulators to thwart deals embolden chief executives to place large acquisition bets.