Prove that `|cosalpha-cosbeta|lt=|alpha-beta|`

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

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

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

Prove that: (cosalpha-cosbeta)^2+(sinalpha-sinbeta)^2=4sin^2((alpha-beta)/2)^(\ )

Prove that (cosalpha+cosbeta)^2+(sinalpha+sinbeta)^2=4cos^2((alpha-beta)/2)dot

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

Prove that: (cosalpha+cosbeta)^2+(sinalpha+sinbeta)^2=4cos^2((alpha-beta)/2)

Prove that: (cosalpha+cosbeta)^2+(sinalpha+sinbeta)^2=4cos^2\ \ ((alpha-beta)/2)

Prove that cosalpha+cosbeta+cosgamma+cos(alpha+beta+gamma)=4cos((alpha+beta)/2)cos((beta+gamma)/2)cos((gamma+alpha)/2)

Prove that cosalpha+cosbeta+cosgamma+cos(alpha+beta+gamma)=4cos((alpha+beta)/2)cos((beta+gamma)/2)cos((gamma+alpha)/2)