Question

一道长方体性质的证明题~长方体一条对角线与同一个顶点的三个侧面所成的角为α,β,γ,则(cosα)^2+(cosβ)^2

Answer 1

用解析几何解

设对角线顶点为原点和点M（a,b,c)

OM^2=a^2+b^2+c^2

(sinα)^2+(sinβ)^2+(sinγ)^2=1

(cosα)^2+(cosβ)^2+(cosγ)^2=3-(sinα)^2+(sinβ)^2+(sinγ)^2=2