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

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 (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 = sin alpha + sin beta + sin gamma = 0 , show that cos 3alpha + cos 3 beta + cos gamma = 3 cos (alpha + beta + gamma) and

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

If cos alpha + cos beta + cos gamma = sin alpha + sin beta + sin gamma = 0 , show that sin 3alpha + sin 3 beta + sin 3gamma = 3 sin (alpha + beta + gamma)

If cos alpha + cos beta + cos gamma = 0 = sin alpha + sin beta + sin gamma then show that cos 3 alpha + cos 3 beta + cos 3 gamma = 3 cos ( alpha + beta + gamma)