Using properties of determinants. Prove that`|sinalphacosalphacos(alpha+delta)sinbetacosbetacos(beta+delta)singammacosgammacos(gamma+delta)|=0`

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

Show that |[sinalpha, cosalpha, cos(alpha+delta)],[sinbeta, cosbeta, cos(beta+delta)],[singamma, cosgamma, cos(gamma+delta)]|=0

Prove that |(sin alpha,cos alpha,sin(alpha+delta)),(sin beta,cos beta,sin(beta+delta)),(sin gamma,cos gamma,sin(gamma+delta))|=0

Without expanding, show that the value of each of the determinants is zero: |sinalphacosalpha"cos"(alpha+delta)sinbetacosbeta"cos"(beta+delta)singammacosgamma"cos"(gamma+delta)|

Without expanding, show that the value of the following determinant is zero: |[sinalpha,cosalpha,cos(a+delta)],[sinbeta,cosbeta,cos(beta+delta)],[singamma,cosgamma,cos(gamma+delta)]|

Without expanding evaluate the determinant |sinalphacosalphasin(alpha+delta)sinbetacosbetasin(beta+delta)singammacosgammasin(gamma+delta)| .

Without expanding evaluate the determinant |[sinalpha,cosalpha,sin(alpha+delta)],[sinbeta,cosbeta,sin(beta+delta)],[singamma,cosgamma,sin(gamma+delta)]|

Without expanding evaluate the determinant |[sinalpha,cosalpha,sin(alpha+delta)],[sinbeta,cosbeta,sin(beta+delta)],[singamma,cosgamma,sin(gamma+delta)]|

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)

Show that the determinant Delta(x) given by Delta(x) = |{:(sin(x+alpha),cos(x+alpha),a+xsinalpha),(sin(x+beta),cos(x+beta),b+xsinbeta),(sin(x+gamma),cos(x+gamma),c+xsingamma):}| is independent of x .