化简 tan(x/2 + π/4)-tan(π/4 - x/2)
来源:百度知道 编辑:UC知道 时间:2024/05/21 23:59:49
化简 tan(x/2 + π/4)-tan(π/4 - x/2)
要过程
要过程
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)=(tanx/2+1)/(1-tanx/2)
tan(π/4-x/2)=(1-tanx/2)/(1+tanx/2)
所以原式通分得:(4tanx/2)/(1-(tanx/2)^2)=2tanx
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