Statement 1: If `cosalpha,cosbeta,a n dcosgamma` are the direction cosines of any line segment, then `cos^2alpha+cos^2beta+cos^2gamma=1.` Statement 2: If `cosalpha,cosbeta,a n dcosgamma` are the direction cosines of any line segment, then `cos2alpha+cos2beta+cos2gamma=1.`

If cosalpha, cosbeta and cosgamma are the direction cosine of a line, then find the value of cos^2alpha+(cosbeta+singamma)(cosbeta-singamma) .

If alpha+beta+gamma=pi , prove that : cos^2 alpha + cos^2 beta + cos^2 gamma+2cosalpha cosbeta cosgamma=1 .

If cosalpha+cosbeta+cosgamma=0 , then prove that cos3alpha+cos3beta+cos3gamma=12cosalphacosbetacosgamma

If the direction angles of a line are alpha, beta and gamma respectively, then cos 2 alpha + cos 2 beta + cos 2gamma is equal to

The value of cos^(2) alpha +cos^(2) beta +cos^(2) gamma is _____ .

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.

A line makes angles alpha,beta,gamma and delta with the diagonals of a cube, prove that cos^2alpha+cos^2beta+cos^2gamma+cos^2delta=4/3

STATEMENT-1 : The angle between the lines whose direction ratios are (1, 2, 3) and (-12, 3, 2) is 90^(@) STAEMENT-2 : The direction cosines of a line whose direction ratios are (3, 4, 12) are (3/13, 4/13, 12/13) . STATEMENT-3 : If cosalpha, cosbeta,cosgamma are the direction cosines of a line then sin^(2)alpha + sin^(2)beta +sin^(2)gamma = 2.

f(alpha,beta) = cos^2(alpha)+ cos^2(alpha+beta)- 2 cosalpha cosbeta cos(alpha+beta) is

A line makes angles alpha,""""beta,""""gamma and delta with the diagonals of a cube, prove that cos^2alpha+cos^2beta+cos^2gamma+cos^2delta=4/3