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

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/07/05 11:56:39

证明tan(3x/2)-tan(x/2)=(2sinx)/(cosx+cos2x)
请各位大侠相助!

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.

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