|[1,cos(alpha-beta),cos alpha],[cos(alpha-beta),1,cos beta],[cos alpha,cos beta,1]|

IF alpha , beta are the roots of the equation ax ^2 + bx +c=0 , then the value of the determinant |(1, cos ( beta - alpha ), cos alpha ),( cos (alpha- beta ),1,cos beta ),( cos alpha , cos beta , 1)|

cos (alpha-beta) quad cos (alpha-beta), cos alpha1, cos betacos alpha, cos beta, 1] |

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

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]|

Without expanding, show that the following determinants vanish: {:|(1,cos(beta-alpha),cos(gamma-alpha)),(cos(alpha-beta),1,cos(gamma-beta)),(cos(alpha-gamma)),cos(beta-gamma),1|

det[[cos alpha cos beta,cos alpha sin beta,-sin alpha-sin beta,cos beta,0sin alpha cos beta,sin alpha sin beta,cos alpha]]

Find the value of f(alpha, beta) =|(cos (alpha + beta), -sin (alpha + beta), cos 2beta),(sin alpha, cos alpha, sin beta),(-cos alpha, sin alpha, cos beta)|