文 [1]给出结论 :在正四棱锥中 ,设侧面与底面所成的二面角为α ,相邻两侧面所成的二面角为 β ,则ｃｏｓβ =-ｃｏｓ2 α .图 1　 (1)式证明用图事实上 ,由ｃｏｓβ =-ｃｏｓ2 α可化为 2ｃｏｓ2 β2 - 1=-ｃｏｓ2 α ,所以 2ｃｏｓ2 β2 =ｓｉｎ2 α ,进而化为ｃｏｓ β2 =ｃ The paper [1] gives the conclusion: In the regular quadratic pyramid, set the dihedral angle formed by the side surface and the bottom surface as α, and the dihedral angle formed by the adjacent two side surfaces is β, then cosβ = -cos2 α . Figure 1 (1 The proof of the formula is in fact cosβ = -cos2 α can be converted to 2cos2 β2 - 1 = -cos2 α, so 2cos2 β2 = sin2 α, and further into cos β2 = c