求证:tan(3x/2)-tan(x/2)=(2sinx)/(cosx+cos2x)

来源:学生作业帮助网 编辑:作业帮 时间:2024/10/05 13:36:49
求证:tan(3x/2)-tan(x/2)=(2sinx)/(cosx+cos2x)
x){F< }#M] İ0*̫H/F6IEj/!L`a[r>P1TH .bhl %&  EQ4 A] roL{:uP+xS[YDŽ竻l @Ջ

求证:tan(3x/2)-tan(x/2)=(2sinx)/(cosx+cos2x)
求证:tan(3x/2)-tan(x/2)=(2sinx)/(cosx+cos2x)

求证:tan(3x/2)-tan(x/2)=(2sinx)/(cosx+cos2x)
tan(3x/2)-tan(x/2)
=sin(3x/2)/cos(3x/2)-sin(x/2)/cos(x/2)(通分)
=[sin(3x/2)cos(x/2)-cos(3x/2)sin(x/2)]/[cos(3x/2)cos(x/2)]
=sin(3x/2-x/2]/[(1/2)(cos2x+cosx)(积化和差)
=2sinx/(cosx+cos2x)
故原式成立.