By David Morgan (Reuters) -Lisa Cook, an economics professor at Michigan State University known for her work on racial and gender inequality, on Tuesday won U.S. Senate confirmation to serve on the Federal Reserve Board, making her the first Black woman to serve on the Fed board in its 109-year history. Cook will join the U.S. central bank as it faces a monumental challenge: reining in 40-year-high inflation that is straining household budgets and sapping U.S. President Joe Biden’s approval ratings without undercutting a historically strong labor market or sending the world’s largest economy i…