If `alpha,beta and gamma` are such that `alpha+beta+gamma=0`, then `|(1,cos gamma,cosbeta),(cosgamma,1,cos alpha),(cosbeta,cos alpha,1)|`

If alpha+beta+gamma=0 ,prove that cosalpha+cosbeta+cosgamma=4cos(alpha/2)cos(beta/2)cos(gamma/2)-1

If cosalpha+cosbeta+cosgamma=0 , then prove that cos3alpha+cos3beta+cos3gamma=12cosalphacosbetacosgamma

If sinalpha+sinbeta+singamma=cosalpha+cosbeta+cosgamma=0, then (A) cos3alpha+cos3beta+cos3gamma=3cos(alpha+beta+gamma) (B) cos 3alpha+cos3beta+cos3gamma=0 (C) sin3alpha+sin3beta+sin3gamma=0 (D) sin3alpha+sin3beta+sin3gamma= 3sin(alpha+beta+gamma)

If alpha,beta, gamma are any three angles , then cos alpha + cos beta - cos gamma - cos (alpha+beta+gamma)=

If alpha, beta, gamma are three real numbers and A=[(1,cos (alpha-beta),cos(alpha-gamma)),(cos (beta-alpha),1,cos (beta-gamma)),(cos (gamma-alpha),cos (gamma-beta),1)] then which of following is/are true ?

If alpha, beta, gamma are three real numbers and A=[(1,cos (alpha-beta),cos(alpha-gamma)),(cos (beta-alpha),1,cos (beta-gamma)),(cos (gamma-alpha),cos (gamma-beta),1)] then which of following is/are true ?

If alpha+beta+gamma=pi , prove that : cos^2 alpha + cos^2 beta + cos^2 gamma+2cosalpha cosbeta cosgamma=1 .

If |{:(1,cos alpha, cos beta),(cos alpha, 1 , cos gamma ),(cos beta, cos gamma , 1):}|=|{:(0,cos alpha, cos beta),(cos alpha , 0 , cos gamma),(cos beta, cos gamma, 0):}| then the value of cos^2 alpha + cos^2 beta + cos^2 gamma is :