If `alpha,beta,gamma` are real numbers, then determinant `Delta=|(sin^2 alpha,cos 2 alpha,cos^2 alpha),(sin^2 beta,cos 2 beta,cos^2 beta),(sin^2 gamma,cos 2 gamma,cos^2 gamma)|`equals

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

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

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

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)|

If Delta = det [[sin alpha, cos alpha, sin alpha + cos alphasin beta, cos alpha, sin beta + cos betasin gamma, cos alpha, sin gamma + cos beta]] then Delta

prove that, |{:(sin^2alpha,sin alpha cosalpha,cos^2alpha),(sin^2beta,sinbetacosbeta,cos^2beta),(sin^2gamma,singammacosgamma,cos^2gamma):}|=-sin(alpha-beta)sin(beta-gamma)sin(gamma-alpha)