If `alpha, beta, gamma` be the direction angles of a straight line, then prove that `sin^(2) alpha+sin^(2) beta+sin^(2) gamma =2`

If alpha, beta , gamma are angles of a triangle then the value of (sin^(2) alpha + sin ^(2) beta+sin ^(2) gamma-2 cos alpha cos beta cos gamma) is-

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 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.

If alpha, beta, gamma are positive acute angles, prove that sin alpha+sin beta+ sin gamma gt sin (alpha+ beta+ gamma)

If (tan (alpha- beta+ gamma))/(tan (alpha+ beta- gamma))=(tan beta)/( tan gamma) , show that either sin (beta- gamma)=0 or sin 2 alpha+ sin 2 beta+ sin 2 gamma=0

If cos^2alpha-sin^2alpha=tan^2beta," then prove that "tan^2alpha=cos^2beta-sin^2beta .

Prove that if two angles alphaandbeta are complementary angles, then sin^(2)alpha+sin^(2)beta=1

Given alpha+beta-gamma=pi, prove that sin^2alpha+sin^2beta-sin^2gamma=2sinalphasinbetacosgammadot

If alpha,beta,gamma are the angles of a triangle and system of equations cos(alpha-beta)x+cos(beta-gamma)y+cos(gamma-alpha)z=0 cos(alpha+beta)x+cos(beta+gamma)y+cos(gamma+alpha)z=0 sin(alpha+beta)x+sin(beta+gamma)y+sin(gamma+alpha)z=0 has non-trivial solutions, then triangle is necessarily a. equilateral b. isosceles c. right angled "" d. acute angled

If cosalpha+cosbeta+cosgamma=0 a n d a l so sinalpha+sinbeta+singamma=0, then prove that cos2alpha+cos2beta+cos2gamma =sin2alpha+sin2beta+sin2gamma=0