A line makes angles `alpha,beta,gammaa n ddelta` with the diagonals of a cube. Show that `cos^2alpha+cos^2beta+cos^2gamma+cos^2delta=4//3.`

If the line makes angles alpha, beta, gamma, delta with four diagonals of a cube, then the value of cos^(2) alpha+cos^(2) beta+cos^(2) gamma+cos^(2) delta is equal to m/3 . Find m.

A straight line L makes angles alpha, beta, gamma and delta with the four diagonals of a cube, prove that, sin^(2)alpha+sin^(2) beta+sin^(2) gamma+sin^(2) delta =4/3

If a line makes angles alpha,betaa n dgamma with three-dimensional coordinate axes, respectively, then find the value of cos2alpha+cos2beta+cos2gammadot

if alpha+beta+gamma=2pi prove that cos^2alpha+cos^2beta+cos^2gamma-2cosalphacosbetacosgamma=1

If cotalphacotbeta=3 ,show that (cos(alpha-beta))/(cos(alpha+beta))=2

If |{:(1,cos alpha, cos beta),(cos alpha, 1 , cos gamma ),(cos beta, cos gamma , 1):}|=|{:(0,cos alpha, cos beta),(cos alpha , 0 , cos gamma),(cos beta, cos gamma, 0):}| then the value of cos^2 alpha + cos^2 beta + cos^2 gamma is : (a) 1 (b) 1/2 (c) 3/8 (d) 9/4

If alpha,beta,gamma "are in A.P. show that" cot beta = (sin alpha - sin gamma)/(cos gamma -cos alpha)

If alpha,beta,gamma are in A.P. show that cot beta=(sin alpha-sin gamma)/(cos gamma-cos alpha)

If sin alpha + sin beta + sin gamma =3, then the value of (cos alpha + cos beta+ cos gamma) is-

If (cosalpha+cosbeta+cosgamma)=0, sinalpha+sinbeta+singamma=0 then show that cos3alpha+cos3beta+cos3gamma=3cos(alpha+beta+gamma)