If `cos(alpha-beta)+cos(beta-gamma)+cos(gamma-alpha)=-3/2` , prove that `cosalpha+cosbeta+cosgamma=s inalpha+s inbeta+s ingamma=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

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

Let cos(alpha-beta) + cos(beta - gamma) + cos(gamma - alpha)= -3/2 , then the value of cos alpha + cos beta + cos gamma is

If cos alpha + cos beta + cos gamma = 3 then sin alpha + sin beta + sin 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 alpha+beta=gamma prove that cos^(2)alpha+cos^(2)beta+cos^(2)gamma=1+2cos alpha cos beta cos gamma

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=0cos(alpha+beta)x+cos(beta+gamma)y+cos(gamma+alpha)z=0sin(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

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

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

The expression cos^(2)(alpha + beta + gamma) + cos^(2)(beta + gamma) + cos^(2)alpha - 2cos alpha cos(beta + gamma)cos(alpha + beta + gamma) is