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),2alphabetagamma delta):}|`=0

Prove that |2alpha+beta+gamma+deltaalphabeta+gammadeltaalpha+beta+gamma+delta2(alpha+beta)(gamma+delta)alphabeta(gamma+delta)+gammadelta(alpha+beta)alphabeta+gammadeltaalphabeta(gamma+delta)+gammadelta(alpha+beta)2alphabetagammadelta|=0

Prove that |((beta+gamma-alpha-delta)^4,(beta+gamma-alpha-delta)^2,1),((gamma+alpha-beta-delta)^4,(gamma+alpha-beta-delta)^2,1),((alpha+beta-gamma-delta)^4,(alpha+beta-gamma-delta)^2,1)|=-64(alpha-beta)(alpha-gamma)(alpha-delta)(beta-delta)(gamma-delta)

If alpha,beta,gamma,delta are the roots of x^(4)+p_(1)x^(3)+p_(2)x^(2)+p_(3)x+p_(4)=0 . Then sum of the products of roots taken two at a time " "A) qquad alpha beta+alpha gamma+alpha delta+beta gamma+beta delta+gamma delta=p_(1) " "B) alpha beta+alpha gamma+alpha delta+beta gamma+beta delta+gamma delta,=p_(2) " "C) alpha beta+alpha gamma+alpha delta+beta gamma+beta delta+gamma delta,=p_(3) " "D) alpha beta+alpha gamma+alpha delta+beta gamma+beta delta+gamma delta=p_(4)

Prove that: | alpha beta gamma alpha^(2)beta^(2)gamma^(2)beta+gamma gamma+alpha alpha+beta|=(alpha-beta)(beta-gamma)(gamma-alpha)(alpha+beta+gamma)

If cos(alpha+beta)sin(gamma+delta)=cos(alpha-beta)sin(gamma-delta), prove that cot alpha cot beta cot gamma=cot delta

Prove that |[alpha,beta,gamma] ,[alpha^2,beta^2,gamma^2] , [beta+gamma, gamma+alpha, beta+alpha]| = (alpha-beta)(beta-gamma)(gamma-alpha)(alpha+beta+gamma)

If |((beta+gamma-alpha -delta)^4 , (beta+gamma-alpha-delta)^2,1),((gamma+alpha-beta-delta)^4, (gamma+alpha-beta-delta)^2,1),((alpha+beta-gamma-delta)^4, (alpha + beta-gamma-delta)^2,1)|=-k(alpha -beta)(alpha -gamma)(alpha-delta)(beta-gamma)(beta-delta)(gamma-delta) , then the value of (k)^(1//2) is ____

Show that | (1,1,1), (alpha ^ 2, beta ^ 2, gamma ^ 2), (alpha ^ 3, beta ^ 3, gamma ^ 3) | = (alpha-beta) (beta-gamma) (gamma-alpha) (alphabeta + betagamma + gammaalpha) |

If cos(alpha+beta)*sin(gamma+delta)=cos(alpha-beta)*sin(gamma-delta) prove that cot alpha cot beta cot gamma=cot delta

Prove that, gammaalpha ^ (2), beta ^ (2), gamma ^ (2) beta + alpha, gamma + alpha, alpha + beta] | = (beta-gamma) (gamma-alpha) (alpha-beta) ( alpha + beta + gamma)