From Longman Business Dictionary
cross-examineˌcross-exˈamine verb [transitiveT]LAW to question a WITNESS very carefully during a court case, especially in order to show that they are not telling the truthYou will get a chance to cross-examine the witness when she has finished giving her evidence.
—cross-examination noun [uncountableU]He conceded under cross-examination that he did know about the letter.