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

|(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.

Without expanding,show that the value of each of the determinants is zero: det[[sin alpha,cos alpha,cos(alpha+delta)sin beta,cos beta,cos(beta+delta)sin gamma,cos gamma,cos(gamma+delta)]]

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

Without expanding evaluate the determinant |sin alpha cos alpha sin(alpha+delta)sin beta cos beta sin(beta+delta)sin gamma cos gamma sin(gamma+delta)|

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)]]

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

sum cos^2 alpha_1=sum cos^2beta_1= sum cos^2 gamma_1=1; sum cosalpha_1 cosbeta_1= sum cosbeta_1 cos gamma_1= sum cos alpha_1 cos gamma_1=0 then |[cos alpha_1, cos alpha_2, cos alpha_3] , [cos beta_1, cos beta_2, cos beta_3] , [cos gamma_1, cos gamma_2, cos gamma_3]|^2= (i)1 (ii)-1 (iii)0 (iv) none of these

Suppose alpha ,beta , gamma in R are such that sin alpha, sin beta , sin gamma ne 0 and Delta = |{:(sin^(2) alpha , sin alpha cos alpha , cos^(2) alpha),(sin^(2) beta , sin beta cos beta , cos^(2) beta),(sin^(2) gamma , sin gamma cos gamma , cos^(2) gamma):}| then Delta cannot exceed