" The value of "|[1,cos(alpha-beta),cos(gamma-alpha)],[cos(alpha-beta),1,cos(beta-gamma)],[cos(gamma-alpha),cos(beta-gamma),1]|" is "

A=[(1, cos (beta-alpha),cos(gamma-alpha)),(cos (alpha-beta), 1, cos(gamma-beta)),(cos (alpha-gamma),cos (beta-gamma),1)]=

det [[1, cos (beta-alpha), cos (gamma-alpha) cos (alpha-beta), 1, cos (gamma-beta) cos (beta-alpha), cos (beta-gamma), 1]] =

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

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|

If alpha,beta "and" gamma are real number without expanding at any stage prove that |{:(1,cos(beta-alpha),cos(gamma-alpha)),(cos(alpha-beta),1,cos(gamma-beta)),(cos(alpha-gamma),cos(beta-gamma),1):}| =0.

If alpha,beta "and" gamma are real number without expanding at any stage prove that |{:(1,cos(beta-alpha),cos(gamma-alpha)),(cos(alpha-beta),1,cos(gamma-beta)),(cos(alpha-gamma),cos(beta-gamma),1):}| =0.