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kuing
Posted 2013-11-19 18:30
设直线与 $x$ 轴夹角为 $\theta$，则
\[AB=\tan\theta+\cot\frac\theta2=f(\theta),\]
求导得
\[f'(\theta)=\sec^2\theta-\frac12\csc^2\frac\theta2,\]
则
\[f'(\theta)=0\iff2\sin^2\frac\theta2=\cos^2\theta\iff\cos\theta=1-\cos^2\theta,\]
解得
\[\cos\theta=\frac{\sqrt5-1}2,\]
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