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

If cos alpha+cos beta+cos gamma=0, then prove that cos3 alpha+cos3 beta+cos3 gamma=12cos alpha cos beta cos gamma

If cos alpha+cos beta+cos gamma=0; then prove that cos3 alpha+cos3 beta+cos3 gamma=12cos alpha cos beta cos gamma

If sinalpha+sinbeta+singamma=cosalpha+cosbeta+cosgamma=0 then prove that cos3alpha+cos3beta+cos3gamma=3cos(alpha+beta+gamma)

If alpha+beta+gamma=0 ,prove that cosalpha+cosbeta+cosgamma=4cos(alpha/2)cos(beta/2)cos(gamma/2)-1

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

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

if alpha+beta+gamma=2pi prove that cos^2alpha+cos^2beta+cos^2gamma-2cosalphacosbetacosgamma=1

If (cosalpha+cosbeta+cosgamma)=0, sinalpha+sinbeta+singamma=0 then show that cos3alpha+cos3beta+cos3gamma=3cos(alpha+beta+gamma)

If secalpha+secbeta+secgamma=0 ,show that (cosalpha+cosbeta+cosgamma)^2=cos^2alpha+cos^2beta+cos^2gamma

If alpha+beta=gamma ,show that cos^2alpha+cos^2beta+cos^2gamma=1+2cosalphacosbetacosgamma