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 with the coordinates axes . If alpha+beta=90^@ then gamma is equal to

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

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 .

Prove that sin^2alpha-sin^4alpha= cos^2alpha-cos^4alpha

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

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

If the normals at alpha, beta,gamma and delta on an ellipse are concurrent then the value of (sigma cos alpha)(sigma sec alpha) I

If cosalpha+cosbeta+cosgamma=0a n da l sosinalpha+sinbeta+singamma=0, then prove that cos2alpha+cos2beta+cos2gamma =sin2alpha+sin2beta+sin2gamma=0 sin3alpha+sin3beta+sin3gamma=3sin(alpha+beta+gamma) cos3alpha+cos3beta+cos3gamma=3cos(alpha+beta+gamma)

If sin beta is the G.M between sin alpha and cos alpha , then cos 2 beta is