立体几何课本第117页有一道习题:如图1,AB和平面α所成角是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_1·cosθ_2=cosθ(1)。此题证明并不难,利用三垂线定理和直角三角形中的边角关系,即可证得。值得指出的是可以引导学生从这个等式中学到更多的东 There is an exercise on page 117 of the three-dimensional geometry textbook: as shown in Figure 1, the angle between AB and plane α is θ_1, AC is within the plane α, and the projection AB′ of AC and AB forms the angle θ_2. Let ∠BAC=θ, and verify that: cosθ_1 Cosθ_2 = cosθ (1). It is not difficult to prove this problem. It can be proved by the use of the triple vertical line theorem and the right angle triangle. It is worth pointing out that students can be guided to learn more from this equation