Prove that `cosalpha+cosbeta+cosgamma(alpha+beta+gamma)=4cos(alpha+beta)/(2)cos(beta+gamma)/2cos(gamma+alpha)/2`

For all value of alpha,beta,gamma prove that ,cosalpha+cosbeta+cosgamma+cos(alpha+beta+gamma)=4cos(alpha+beta)/2*cos(beta+gamma)/2*cos(gamma+alpha)/2

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

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

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)

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=sin alpha+sin beta+sin gamma=0 , and cos(alpha-beta)+cos(beta-gamma)+cos(gamma-alpha)=6K , K in R , then K is equal to :

Prove that : cos^2 (beta-gamma) + cos^2 (gamma-alpha) + cos^2 (alpha-beta) =1+2cos (beta-gamma) cos (gamma-alpha) cos (alpha-beta) .

If alpha + beta + gamma = 2 theta , prove that cos theta + cos(theta- alpha) + cos(theta- beta) + cos(theta -gamma) = 4(cos (alpha/2) cos (beta/2) cos (gamma/2))

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