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

cos(alpha-beta)+cos(beta-gamma)+cos(gamma-alpha)=-(3)/(2), prove that cos alpha+cos beta+cos gamma=sin alpha+sin beta+sin gamma=0

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

cos(alpha-beta)+cos(beta+gamma)+cos(gamma-alpha)=-(3)/(2) prove that: cos alpha+cos beta+cos gamma=sin alpha+sin beta+sin gamma=0

If cos (alpha - beta) + cos (beta - gamma) + cos (gamma - alpha) = (-3)/(2) then prove that cos alpha + cos beta+ cos gamma = sin alpha + sin beta + sin gamma = 0 .

cos(beta-gamma)+cos(gamma-alpha)+cos(alpha-beta)=-3/2 show that cosalpha+cosbeta+cosgamma=0 and sinalpha+sinbeta+singamma=0 also cos(beta-gamma)=cos(gamma-alpha)=cos(alpha-beta)=-1/2 .

If cos (beta - gamma) + cos (gamma - alpha) + cos (alpha - beta) = -3/2, "show that", cos alpha + cos beta + cos gamma = 0 "and" sin alpha + sin beta + singamma = 0."Hence deduce that," cos (beta - gamma) = cos (gamma - alpha) = cos (alpha - beta) = -1/2.

If sinalpha+sinbeta+singamma=cosalpha+cosbeta+cosgamma=0, then (A) cos3alpha+cos3beta+cos3gamma=3cos(alpha+beta+gamma) (B) cos 3alpha+cos3beta+cos3gamma=0 (C) sin3alpha+sin3beta+sin3gamma=0 (D) sin3alpha+sin3beta+sin3gamma= 3sin(alpha+beta+gamma)

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