求证:(sinX+cosX+1)/(1+cosX)=1+tan(X/2)
求证:(sinX+cosX+1)/(1+cosX)=1+tan(X/2)
数学人气:506 ℃时间:2020-03-31 08:55:28
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证明:把分子拆开,化简,再用倍角公式即可 原式=sinx/(1+cosx)+(1+cosx)/(1+cosx) =1+sinx/(1+cosx) =1+2sin(x/2)cos(x/2)/2cos^2(x/2) =1+sin(x/2)/cos(x/2) =1+tan(x/2) 命题得证
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