[" if "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 .

If cos alpha+ cos beta + cos gamma = sin alpha+ sin beta +sin gamma= 0 , then :

If cos alpha + cos beta + cos gamma = 3 then sin alpha + sin beta + sin gamma =

cos alpha + cos beta + cos gamma + cos ( alpha + beta + gamma ) =

If cos alpha + cos beta + cos gamma =3 , " then " sin alpha + sin beta + sin gamma =

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 cos alpha+cos beta+cos gamma=0=sin alpha+sin beta+sin gamma then prove that cos2 alpha+cos2 beta+cos2 gamma=sin2 alpha+sin2 beta+sin2 gamma=0

cos (alpha + beta) cos gamma-cos (beta + gamma) cos alpha = sin beta sin (gamma-alpha)

If cos alpha+ cos beta+ cos gamma + cos alpha cos beta cos gamma=0 , show that sin alpha (1+ cos beta cos gamma)=+- sin beta sin gamma .

If cos alpha+cos beta+cos gamma=0 and also sin alpha+sin beta+sin gamma=0 then prove that