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If alpha, beta & gamma real numbers, the...

If `alpha, beta & gamma` real numbers, then value of `|(1,cos(beta-alpha),cos(gamma-alpha)),(cos(alpha-beta),1,cos(gamma-beta)),(cos(alpha-gamma),cos(beta-gamma),1)|` is equal to

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The correct Answer is:
`0.00`
Write 1 as `sin^(2)alpha+cos^(2)alpha+cos^(2)alpha` etc. to get
`|(sin^2alphacos^2alpha,cosbetacos alpha,cosgammacos alpha+singammasin alpha),(cos alpha cos beta+sinalphasin beta,cos^2beta+sin^2beta,cosgammacosbeta+singammasinbeta),(cosalphacosgamma+sinalphasingamma,cosbetacosgamma+sinbetasingamma,sin^2gamma+cos^2gamma)|`
can be factorized into 2 determinant
`|(cosalpha,sinalpha,x),(cosbeta,sinbeta,x),(cosgamma,singamma,x)||(cosalpha,cos beta,cos gamma),(sin alpha,sinbeta,sin gamma),(x,x,x)|=0`.
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