作业帮化简 tan(x/2 + π/4)-tan(π/4 - x/2)
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/08/23 08:23:47
化简 tan(x/2 + π/4)-tan(π/4 - x/2)
tan(x/2 + π/4)-tan(π/4 - x/2)
=tan(x/2+π/4)-cot[π/2-(π/4-x/2)]
=tan(x/2+π/4)-cot(x/2+π/4)
=sin(x/2+π/4)/cos(x/2+π/4)-cos(x/2+π/4)/sin(x/2+π/4)
={[sin(x/2+π/4)]^2-[cos(x/2+π/4)]^2}/[sin(x/2+π/4)cos(x/2+π/4)]
=-cos(x+π/2)/[sin(x+π/2)/2]
=-2cot(x+π/2)
=tan(x/2+π/4)-cot[π/2-(π/4-x/2)]
=tan(x/2+π/4)-cot(x/2+π/4)
=sin(x/2+π/4)/cos(x/2+π/4)-cos(x/2+π/4)/sin(x/2+π/4)
={[sin(x/2+π/4)]^2-[cos(x/2+π/4)]^2}/[sin(x/2+π/4)cos(x/2+π/4)]
=-cos(x+π/2)/[sin(x+π/2)/2]
=-2cot(x+π/2)
1)tan(x/2+π/4)+tan(x/2-π/4)=2tanx
tan（X/2+π/4)+tan（x/2-π/4）=2tanx?
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tan(x/2+ π4)+tan(x/2- π/4)=2tanx
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