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Prove that : cos^2alpha+cos^2(alpha+beta...

Prove that : `cos^2alpha+cos^2(alpha+beta)-2cosalphacosbetacos(alpha+beta)=sin^2beta`

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`L.H.S. = cos^2 alpha + cos^2 (alpha+beta) - 2cos alpha cosbeta cos(alpha+beta)`
`=cos^2 alpha + cos(alpha+beta)(cos(alpha+beta) - 2cos alpha cosbeta)`
`=cos^2 alpha + (cosalphacosbeta - sinalphasinbeta)(cosalphacosbeta - sinalphasinbeta - 2cos alpha cosbeta)`
`=cos^2 alpha + (cosalphacosbeta - sinalphasinbeta)(-cosalphacosbeta - sinalphasinbeta )`
`=cos^2 alpha - (cosalphacosbeta - sinalphasinbeta)(cosalphacosbeta + sinalphasinbeta )`
`=cos^2 alpha - (cos^2alphacos^2beta - sin^2alphasin^2beta)`
`=cos^2 alpha (1-cos^2beta) + sin^2alphasin^2beta`
`=cos^2alphasin^2beta +sin^2alphasin^2beta`
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