Determine the values of `alpha ,beta , gamma ` when `[{:( 0, 2beta, gamma),( alpha ,beta, -gamma),( alpha ,-beta, gamma):}]` is orthogonal.

Determine the values of alpha, beta, gamma when [{:(0,2sinbeta,tan gamma),(cos alpha, sin beta,-tan gamma),(cos alpha, -sin beta, tan gamma):}] is orthogonal.

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

If alpha, beta, gamma are the cube roots of 8 , then |(alpha,beta,gamma),(beta,gamma,alpha),(gamma,alpha,beta)|=

If [(0,2beta,gamma),(alpha,beta,-gamma),(alpha,-beta,gamma)] is orthogonal, then find the value of 2alpha^(2)+6beta^(2)+3gamma^(2).

If alpha,beta,gamma are the roots of px^(2)+qx^(2)+r=0 then the value of the determinant det[[alpha beta,beta gamma,gamma alphabeta gamma,gamma alpha,alpha betagamma alpha,alpha beta,beta gamma]] is p b.q c.0 d.r

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

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

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