A line makes angles `alpha, beta, gamma, delta` with the four main diagonals of a cube. Prove that `cos^2alpha+cos^2beta+cos^2gamma+cos^2delta=4/3`

If alpha,beta,gamma be direction angles of a line, what is the value of sin^2alpha+sin^2beta+sin^2gamma .

If sin alpha + sin beta +sin gamma=0 =cos alpha+cos beta+cos gamma=0 "Show that" sin^2 alpha+sin^2beta+sin^2gamma=cos^2 alpha+ cos^2beta+cos^2gamma=3/2

Prove that the measure of the angle between two main diagonals of a cube is cos^(-1)frac[1][3] .

Given cos alpha+cos beta +cos gamma=sin alpha+sin beta +sin gamma=0 Show that cos3 alpha+cos3 beta+cos 3gamma = 3 cos(alpha +beta+ gamma)