[" Q.3.Prove that: "],[" (i) "cos^(2)alpha+cos^(2)beta+cos^(2)gamma=1]

If cos alpha + cos beta + cos gamma = 0 sin alpha + sin beta + sin gamma , Prove that cos^(2) alpha + cos^(2) beta + cos^(2) gamma = 3/2 = sin^(2) alpha + sin^(2) beta + sin^(2) gamma .

If alpha+beta=gamma prove that cos^(2)alpha+cos^(2)beta+cos^(2)gamma=1+2cos alpha cos beta cos gamma

If cos alpha + cos beta+ cos gamma = 0 = sin alpha + sin beta+sin gamma show that sin^(2)alpha + sin^(2) beta + sin^(2) gamma =cos^(2)alpha +cos^(2) beta + cos^(2) gamma =3/2

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

If alpha, beta , gamma are direction-angles of a line, prove that (i) cos2alpha + cos 2 beta +cos2 gamma+ 1 = 0 . (ii) cos 2 alpha + cos 2 beta + cos 2 gamma = -1 .

If cos alpha + cos beta + cos gamma = 0 = sin alpha + sin beta + sin gamma then (a) sin ^ (2) alpha + sin ^ (2) beta + sin ^ (2) gamma = (3) / ( 2) (b) sin ^ (2) alpha + sin ^ (2) beta + sin ^ (2) gamma = (3) / (4) (c) cos ^ (alpha) + cos ^ (2) beta + cos ^ (2) gamma = (3) / (2) (d) cos ^ (2) alpha + cos2 beta + cos2 gamma = -1

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