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

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 Delta=|(sinalpha,cosalpha,sin(alpha+delta)),(sinbeta,cosbeta,sin(beta+delta)),(singamma,cosgamma,sin(gamma+delta))| then Delta is independent of a) delta only b) alpha, beta, gamma only c) alpha,beta,gamma,delta d)None of these

Evaluate Delta=|[0, sin alpha, -cos alpha],[ -sin alpha, 0 , sin beta],[ cos alpha, -sin beta, 0]|

If alpha , beta , lambda are three real numbers and A=[(1,cos(alpha-beta),cos(alpha-gamma)),(cos(beta-alpha),1,cos(beta-gamma)),(cos(gamma-alpha),cos(gamma-beta),1)] , then which of following is not true A)A is singular B)A is symmetric C)A is orthogonal D)A is not invertible

Evaluate |[cos alpha cos beta, cos alpha sin beta, -sin alpha],[ -sin beta, cos beta, 0],[ sin alpha cos beta, sin alpha sin beta, cos alpha]|

A line makes acute angles of alpha, beta and gamma with the co-ordinae axes such that cos alpha cos beta = cos beta cos gamma = (2)/(9) and cos gamma cos alpha = (4)/(9), then cos alpha + cos beta + cos gamma is equal to : a) (25)/(9) b) (5)/(9) c) (5)/(3) d) (2)/(3)

|(1,cosalpha,cosbeta),(cosalpha,1,cosgamma),(cosbeta,cosgamma,1)|=|(0,cosalpha,cosbeta),(cosalpha,0,cosgamma),(cosbeta,cosgamma,0)|" if " cos^(2)alpha+cos^(2)beta+cos^(2)gamma= a)1 b)2 c) 3//2 d) 1//2