分类：教育/科学-学习帮助
问题：求证ＴＡＮ３Ｘ／２－ＴＡＮＸ／２＝２ＳＩＮＸ／（ＣＯＳＸ加ＣＯＳ? 
回答：求证：tg(3x/2)-tg(x/2)=2sinx/(cosx+cos2x)
证明：
tg(3x/2)-tg(x/2)
=[sin(3x/2)/cos(3x/2)]-[sin(x/2)/cos(x/2)]
=[sin(3x/2)*cos(x/2)-sin(x/2)*cos(3x/2)]/cos(3x/2)*cos(x/2) 
=sin[(3x/2)-(x/2)]/(1/2){[cos[(3x/2)+(x/2)]+cos[(3x/2)-(x/2)]} 
=sinx/[(1/2)(cos2x+cosx)]
=2sinx/(cos2x+cosx)
得证