[" 24.(i) If "Delta=|[sin alpha,cos alpha,sin(alpha+delta)],[sin beta,cos beta,sin(beta+delta)],[sin gamma,cos gamma,sin(gamma+delta)]|" then prove that "Delta" is independent of "],[alpha,beta,gamma" and "delta]

|(sin alpha, cosalpha,sin(alpha+delta)),(sinbeta, cos beta,sin(beta+delta)),(singamma,cosgamma,sin(gamma+delta))|=

If /_\ = |[sinalpha, cosalpha, sin(alpha+delta)],[sinbeta, cosbeta, sin(beta+delta)],[singamma, cosgamma, sin(gamma+delta)]| then prove that /_\ is independent of alpha, beta, gamma and delta.

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

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

Prove that det [[sin alpha, cos alpha, sin (alpha + delta) sin beta, cos beta, sin (beta + delta) sin gamma, cos gamma, sin (gamma + delta)]] = 0

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

If Delta=|(sin alpha, cos alpha, sin alpha+cos beta),(sin beta, cos alpha, sin beta+cos beta),(sin gamma, cos alpha, sin gamma+cos beta)| then Delta equals

{:|( sin alpha , cos alpha ,cos (alpha +delta) ),( sinbeta, cos beta,cos (beta+delta )),(sin gamma , cos gamma , cos ( gamma +delta ))|:}=0

Without expanding evaluate the determinant det[[sin alpha,cos alpha sin(alpha+delta)sin beta,cos beta,sin(beta+delta)sin gamma,cos gamma,sin(gamma+delta)]]