第一知识网
www.001rz.com求证：（sin2x)(1+tanx*tan(x/2))/2cosx=tanx
日期：2021-04-24 04:43:53 人气：99
由倍角公式及半角公式有：
sin(2x)=2sin(x)cos(x)
tan(x/2)=(1-cos(x))/sin(x)
则，原式 = [2sin(x)cos(x)/2cos(x)]*{1+[sin(x)/cox(x)]*[(1-cos(x))/sin(x)]} = sin(x)*(1+(1-cos(x))/cos(x)) = sin(x)/cos(x) = tan(x)
sin(2x)=2sin(x)cos(x)
tan(x/2)=(1-cos(x))/sin(x)
则，原式 = [2sin(x)cos(x)/2cos(x)]*{1+[sin(x)/cox(x)]*[(1-cos(x))/sin(x)]} = sin(x)*(1+(1-cos(x))/cos(x)) = sin(x)/cos(x) = tan(x)