If `alpha,beta,gamma` are the direction angles of a line
(i)Show that `sin^2 alpha + sin^2 beta +sin^2 gamma=2`.
(ii)Find the value of `cos2alpha +cos2beta+cos2gamma`.

If aplha, beta, gamma are the directional angles of a vector then sin^(2)aplha + sin^(2) beta+sin^(2) gamma .

Let alpha, beta, gamma be the measures of angle such that sin alpha+sin beta+sin gamma ge 2 . Then the possible value of cos alpha + cos beta+cos gamma is

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.

Prove that 2 sin^2 beta + 4 cos(alpha + beta) sin alpha sin beta + cos 2(alpha + beta) = cos 2alpha

If cos alpha + cos beta =0 = sin alpha + sin beta , then cos 2 alpha + cos 2 beta is equal to

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 alpha,beta,a n dgamma are the an gles which a directed line makes with the positive directions of the co-ordinates axes, then find the value of sin^2alpha+sin^2beta+sin^2gammadot

sin alpha+sinbeta=(1)/(4) and cos alpha+cos beta=(1)/(3) the value of sin(alpha+beta)

If cos alpha + cos beta + cos gamma = sin alpha + sin beta + sin gamma = 0 , show that sin 3alpha + sin 3 beta + sin 3gamma = 3 sin (alpha + beta + gamma)