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 cos alpha+cos beta+cos gamma=0, then prove that cos3 alpha+cos3 beta+cos3 gamma=12cos alpha cos beta cos gamma

If alpha+beta=gamma prove that cos^(2)alpha+cos^(2)beta+cos^(2)gamma=1+2cos alpha cos beta cos gamma

If cos alpha+cos beta+cos gamma=0; then prove that cos3 alpha+cos3 beta+cos3 gamma=12cos alpha cos beta cos gamma

If alpha,beta and gamma are angles such that tan alpha+tan beta+tan gamma=tan alpha tan beta tan gamma and x=cos alpha+i sin alpha,y=cos beta+i sin beta and z=cos gamma+i sin gamma then the value of xyz is

If alpha,beta,gamma are acute angle such that cos alpha=tan beta,cos beta=tan gamma and cos gamma=tan alpha then

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 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 ?