Prove that `|{:(alpha,beta,gamma),(theta,phi,psi),(lambda,mu,nu):}|=|{:(beta,mu,phi),(alpha,lambda,theta),(gamma,nu,psi):}|.`

If alpha+beta+gamma=2 pi, then

Distance of the point (alpha, beta, gamma) from the y-axis is

Reflection of the point (alpha, beta, gamma) in XY plane is

Using properties of determinants prove that : {:|( alpha , alpha ^(2) , beta +gamma ),( beta , beta ^(2) , gamma +alpha ),( gamma , gamma ^(2) ,alpha +beta ) |:} =(beta -gamma ) (gamma -alpha ) (alpha -beta ) (alpha +beta +gamma )

Reflexion of the point (alpha, beta, gamma) in XY plane is

If alpha,beta,gammain(0,pi/2) , then (sin(alpha+beta+gamma))/(sinalpha+sinbeta+singamma) is :

If alpha , beta , gamma are the roots of x^3+px+q=0 , then the value of the determine |(alpha,beta,gamma),(beta,gamma,alpha),(gamma,alpha,beta)| is

If alpha, beta, gamma are the roots of the cubic x^(3)-px^(2)+qx-r=0 Find the equations whose roots are (i) beta gamma +1/(alpha), gamma alpha+1/(beta), alpha beta+1/(gamma) (ii) (beta+gamma-alpha),(gamma+alpha-beta),(alpha+beta-gamma) Also find the valueof (beta+gamma-alpha)(gamma+alpha-beta)(alpha+beta-gamma)