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)`

Using properties of determinants, prove that |[sinalpha,cosalpha,cos(alpha+delta)],[sinbeta,cosbeta,cos(beta+delta)],[singamma,cosgamma,cos(gamma+delta)]| = 0

Consider Delta=|(alpha,beta,gamma),(alpha^2,beta^2,gamma^2),(beta+gamma,gamma+alpha,alpha+beta)| Show that Delta=(alpha-beta)(beta-gamma)(gamma-alpha)(alpha+beta+gamma) .

If alpha+beta =pi//2andbeta+gamma=alpha , then tanalpha equals

Consider Delta=|(alpha,beta,gamma),(alpha^2,beta^2,gamma^2),(beta+gamma,gamma+alpha,alpha+beta)| Apply R_3rarrR_1+R_3

Prove that |(2,alpha+beta+gamma+delta,alphabeta+gammadelta),(alpha+beta+gamma+delta,2(alpha+beta)(gamma+delta),alpha beta(gamma+delta)+gamma delta(gamma+beta)),(alpha beta+gamma delta,alpha beta(gamma+delta)+gammadelta(alpha+beta),2alphabeta gamma delta)| = 0

|(alpha,-beta,0),(0,alpha,beta),(beta,0,alpha)|=0 , then

Let A=[(0,2beta,gamma),(alpha,beta,-gamma),(alpha,-beta,gamma)] be 3xx3 matrix If A^T.A=6I, then alpha,beta and gamma is -

Let A=[(0,2beta,gamma),(alpha,beta,-gamma),(alpha,-beta,gamma)] be 3xx3 matrix Find A^T

If alpha, beta, gamma in [0, pi]"and if" alpha, beta, gamma are in AP, then (sin alpha - sin gamma)/(cos gamma - cos alpha) is equal to