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

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 a n d a l so sinalpha+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 cos alpha + cos beta + cos gamma = 0 and also sin alpha + sin beta + sin gamma= 0, then prove that: cos 3 alpha + cos 3beta + cos 3gamma = 3 cos (alpha + beta + gamma)

If cosalpha+cosbeta=0=sinalpha+sinbeta , then prove that cos2alpha +cos2beta=-2cos(alpha +beta) .

If cosalpha+cosbeta=0=s inalpha+s inbeta, then prove that cos2alpha+cos2beta=-2cos(alpha+beta)dot

If alpha, beta, gamma are the angles which a line makes with the coordinate axes ,then (A) sin^2alpha=cos^2beta+cos^2gamma (B) cos^2alpha+cos^2beta+cos^2gamma=2 (C) cos^2alpha+cos^2beta+cos^2gamma=1 (D) sin^2alpha+sin^2beta=1+cos^2gamma

If cosalpha+cosbeta=0=sinalpha+sinbeta , then prove that cos2alpha+cos2beta+2cos(alpha+beta)=0

If cos(alpha-beta)+cos(beta-gamma)+cos(gamma-alpha)=-3/2 , prove that cosalpha+cosbeta+cosgamma=sinalpha+sinbeta+singamma=0

If alpha,beta and gamma are such that alpha+beta+gamma=0 , then |(1,cos gamma,cosbeta),(cosgamma,1,cos alpha),(cosbeta,cos alpha,1)|

If alpha,beta and gamma are such that alpha+beta+gamma=0 , then |(1,cos gamma,cosbeta),(cosgamma,1,cos alpha),(cosbeta,cos alpha,1)|