Prove that `sum_(alpha+beta+gamma = 10) (10 !)/(alpha!beta!gamma!)=3^(10)dot`

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

Prove that: | alpha beta gamma alpha^(2)beta^(2)gamma^(2)beta+gamma gamma+alpha alpha+beta|=(alpha-beta)(beta-gamma)(gamma-alpha)(alpha+beta+gamma)

Prove that: sin alpha+sin beta+sin gamma-sin(alpha+beta+gamma)=4sin((alpha+beta)/(2))*sin((beta+gamma)/(2))*sin((gamma+alpha)/(2))

Prove that: sin alpha+sin beta+sin gamma-sin(alpha+beta+gamma)=4sin((alpha+beta)/(2))sin((beta+gamma)/(2))sin((gamma+alpha)/(2))

If alpha,beta,gamma,in(0,(pi)/(2)), then prove that (si(alpha+beta+gamma))/(sin alpha+sin beta+sin gamma)<1

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

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