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

If cos(alpha+beta)*sin(gamma+delta)=cos(alpha-beta)*sin(gamma-delta), prove that cotalphacotbetacotgamma=cotdelta

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) .

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 cos(alpha+beta)sin(gamma+delta)="cos"(alpha-beta)"sin"(gamma-delta) , prove that cotalphacotbetacotgamma=cotdelta

If alpha + beta + gamma = pi , show that : tan (beta+gamma-alpha) + tan (gamma+alpha-beta) + tan (alpha+beta-gamma) = tan (beta+gamma-alpha) tan (gamma+alpha-beta) tan (alpha+beta-gamma)

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)=

The value of |{:(betagamma,betagamma'+beta'gamma,beta'gamma'),(gammaalpha,gammaalpha'+gamma'alpha,gamma'alpha'),(alphabeta,alphabeta'+alpha'beta,alpha'beta'):}| is

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

If 2x^(3) + 3x^(2) + 5x +6=0 has roots alpha, beta, gamma then find alpha + beta + gamma, alphabeta + betagamma + gammaalpha and alpha beta gamma