By Howard Schneider and Ann Saphir WASHINGTON (Reuters) – New Federal Reserve Governor Lisa Cook on Thursday added her voice squarely to the U.S. central bank’s broad consensus for continued interest rate hikes, as other policymakers joined to reiterate they see no let-up in the monetary tightening. U.S. inflation “remains stubbornly and unacceptably high, and data over the past few months show that inflationary pressures remain broad-based,” requiring continued rate increases to be sure it begins falling, Cook said in her first public remarks on monetary policy since joining the Fed’s Washing…