Question

Refer the attached picture. Answer in a short way.

Shortest method needed. ​

Answer 1

Step-by-step explanation:

Let each side of a cube be a unit

Diagonal of cube = √3a unit

If we assume,

A cube of unity then,

a=1unit and diagonal =√3

cos(alpha) = base / hypotenuse

cos(beta) = base / hypotenuse

cos(gama) = base / hypotenuse

cos(delta) = base / hypotenuse

Here base in all case will be 1 unit and hypotenuse will be √3 unit

Putting the value of all this functions in the question we get

(1/√3)^2+(1/√3)^2+(1/√3)^2+(1/√3)^2

1/3+1/3+1/3+1/3

4/3 which is RHS

Hence Proved