Prove that `|{:(2,,alpha+beta+gamma+delta,,alphabeta+gammadelta),(alpha+beta+gamma+delta,,2(alpha+beta)(gamma+delta),,alphabeta(gamma+delta)+gammadelta(alpha+beta)),(alphabeta+gammadelta,,alphabeta(gamma+delta)+gammadelta(alpha+beta),,2alphabetagammadelta):}|=0`

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)

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

If alpha+beta+gamma=2 pi, then

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 )

If cos ^(-1) alpha+cos ^(-1) beta+cos ^(-1) gamma=3 pi then alpha(beta+gamma)+beta(gamma+alpha)+gamma(alpha+beta)=

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

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+a x^2+b=0 then the value of [[alpha , beta , gamma],[beta , gamma , alpha],[gamma , alpha , beta]] is

If 102! =2^(alpha)*3^(beta)*5^(gamma)*7^(delta) …, then

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