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六年制重点中学高中数学教材第二册第100页总复习参考题第3题: 如图,AB和平面a所成的角是θ_1,AC在平面a内,AC和AB的射影AB′成角θ_2,设∠BAC=θ,求证:cosθ_1cosθ_2=cosθ。 (I) 该命题可以看成三垂线定理的推广,在立体几何中有广泛的应用。一为了突出图形的特点,可以把上述命题改写成如下形式: 从直二面角棱上一点在两个面内任引两条射线,则射线与棱的夹角的余弦之积等于这两条射线夹角的余弦。用它来解决一类折叠成直二面角的立几题往往十分简捷。
6-year Key Middle School High School Mathematics Teaching Book Volume 2 Page 100 Total Review Reference Question 3: As shown in the figure, the angle formed by AB and plane a is θ_1, AC is in plane a, and the projection of AC and AB AB′ Angle θ_2, set ∠BAC=θ, verify: cosθ_1cosθ_2=cosθ. (I) This proposition can be seen as a generalization of the tri- perpendicular line theorem, which has a wide range of applications in stereo geometry. In order to highlight the characteristics of the graph, the above propositions can be rewritten as follows: From the point on the straight dihedral, any two rays in any two planes, then the product of the cosine of the angle between the ray and the rib is equal to the two The cosine of the angle of the ray. It is very simple to use it to solve a class of questions that fold into straight dihedral angles.