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

If cos alpha + cos beta + cos gamma = 0 and also sin alpha + sin beta + sin gamma= 0, then prove that: cos 3 alpha + cos 3beta + cos 3gamma = 3 cos (alpha + beta + gamma)

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 show that cos 3 alpha + cos 3 beta + cos 3 gamma = 3 cos ( alpha + beta + gamma)

If x=r cos alpha cos beta cos gamma , y= cos alpha cos beta sin gamma , z= r sin alpha cos beta , mu = r sin beta " then " x^(2)+y^(2) + z^(2)+mu^(2)=

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

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

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