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本刊90年3期《一道值得重视的立体几何习题》、92年2期《一个值得重视的二面角公式》讨论了立体几何中的一个习题: “AB和平面α所成的角是θ_1,AC在平面α内,AC和AB的射影AB′成角θ_2,设∠BAC=θ,求证:cosθ_1cosθ_2=cosθ”的应用和推广,很有教益,也非常重要。笔者认为,这习题之所以重要,不是没有涉及二面角,而是把直二面角的存在与面角的计算公式:
A problem worthy of attention of the three-dimensional geometry exercises in the 90th issue of the journal, Issue 3, and an important dihedral formula of the year 92, discussed an exercise in three-dimensional geometry: “The angle between the AB and the plane α is θ_1 , AC in the plane α, AC and AB projection AB’ angle θ_2, set ∠BAC = θ, verification: cosθ_1cosθ_2 = cosθ, the application and promotion, very helpful, it is also very important. The author believes that the reason why this exercise is important is not that it does not involve the dihedral angle, but rather the calculation formula for the presence and face angle of the straight dihedral angle: