等式左边=2sinxcosx/[sinx+(cosx-1)][sinx-(cosx-1)]=2sinxcosx/[sin^2x-(cosx-1)^2]=2sinxcosx/(sin^2x-cos^2x+2cosx-1)=2sinxcosx/(2cosx-2cos^2x)=sinx/(1-cosx)=2sin(x/2)cos(x/2)/[1-2cos^2(x/2)+1]=sin(x/2)cos(x/2)/[1-cos^2(x/2)]=sin(x/2)cos(x/2)/sin^2(x/2)=cot(x/2)
过程尽量给你写的很详细了,你要是变角公式很熟练的话,中间很多步可以省略直接得出答案哈