`|(1,cos(beta-alpha),cos(gamma-alpha)), (cos(alpha-beta),1,cos(gamma-beta)), (cos(beta-alpha), 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.

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, gamma 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/are true ?

If cos (beta-gamma)+cos(gamma-alpha)+cos(alpha-beta)=-(3)/(2) then

Prove that : cos^2 (beta-gamma) + cos^2 (gamma-alpha) + cos^2 (alpha-beta) =1+2cos (beta-gamma) cos (gamma-alpha) cos (alpha-beta) .

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

Consider the vectors hat i+cos(beta-alpha alpha)hat j+cos(gamma-alpha)hat k,cos(alpha-beta)hat i+hat j+cos(gamma-beta)hat kand cos(alpha-gamma)hat i+cos(beta-gamma)hat k+a where alpha,beta, and gamma are different angles.If these vectors are coplanar,show that a is independent of alpha,beta and gamma