`cos(beta-gamma)+cos(gamma-alpha)+cos(alpha-beta)=-3/2` show that `cosalpha+cosbeta+cosgamma=0` and `sinalpha+sinbeta+singamma=0` also `cos(beta-gamma)=cos(gamma-alpha)=cos(alpha-beta)=-1/2`.

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.

Let A and B denote the statements A: cos alpha+cos beta+cos gamma=0 ,B: sin alpha+sin beta+sin gamma=0 if cos(beta-alpha)+cos(gamma-alpha)+cos(alpha-beta)=(-3/2) then

If (cosalpha+cosbeta+cosgamma)=0, sinalpha+sinbeta+singamma=0 then show that cos3alpha+cos3beta+cos3gamma=3cos(alpha+beta+gamma)

If " "cos(alpha - beta) + 1 = 0," show that ", cosalpha + cos beta = 0 " and " sin alpha + sin beta = 0.

If cos beta cos (gamma- alpha)= cos (alpha- beta+ gamma) , prove that cot alpha+ cot y= 2cot beta

if alpha+beta+gamma=2pi prove that cos^2alpha+cos^2beta+cos^2gamma-2cosalphacosbetacosgamma=1

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 (cosalpha+cosbeta+cosgamma)=0, sinalpha+sinbeta+singamma=0 then show that sin3alpha+sin3beta+sin3gamma=3sin(alpha+beta+gamma)

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

If cotalphacotbeta=3 ,show that (cos(alpha-beta))/(cos(alpha+beta))=2