Express `cos alpha + cos beta + cos gamma+ cos ( alpha+beta+gamma)` as the product of three cosines.

Prove that cos alpha + cos beta + cos gamma + cos (alpha + beta + gamma) = 4 cos"" (alpha + beta)/(2) cos ""(beta + gamma)/(2) cos ""(gamma + alpha)/(2) .

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

The expression cos^(2)(alpha + beta + gamma) + cos^(2)(beta + gamma) + cos^(2)alpha - 2cos alpha cos(beta + gamma)cos(alpha + beta + gamma) is (a) independent of alpha (b) independent of beta (c) dependent on gamma only (d) dependent on 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

For all values of alpha,beta,gamma prove that: cos alpha + cos beta+ cos gamma+ cos(alpha+beta+gamma) ="4cos"(alpha+beta)/2cdot"cos" (beta+gamma)/2cdot"cos"(gamma+alpha)/2

If cos alpha + cos beta + cos gamma = 0 then cos 3alpha + cos 3beta + cos 3gamma = lambda cos alpha *cos beta*cos gamma where lambda is equal to

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)