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prove that,|{:(sin^2alpha,sin alpha cosa...

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)`

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The correct Answer is:
`=-sin(alpha-beta)sin(beta-gamma)sin(gamma-alpha)`
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