cos^2 alfa + cos^2(alfa+ beta) -2cos alfa cos beta cos(alpha+beta)=sin^2 beta
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cos^2α+cos^2(α+β)-2cosαcosβcos(α+β)
=cos^2α+cos^2(α+β)-{cos(α+β)+cos(α-β) }cos(α+β)
=cos^2α+cos^2(α+β)-{cos^2(α+β)+cos(α-β)*cos(α+β)}
=cos^2α+cos^2(α+β)-cos^2(α+β)-cos(α-β)*cos(α+β)}
=cos^2α-cos(α-β)*cos(α+β)
=cos^2α-cos^2α+sin^2β=sin^2β (since cos(α-β)*cos(α+β)=cos^2α-sin^2β)
=cos^2α+cos^2(α+β)-{cos(α+β)+cos(α-β) }cos(α+β)
=cos^2α+cos^2(α+β)-{cos^2(α+β)+cos(α-β)*cos(α+β)}
=cos^2α+cos^2(α+β)-cos^2(α+β)-cos(α-β)*cos(α+β)}
=cos^2α-cos(α-β)*cos(α+β)
=cos^2α-cos^2α+sin^2β=sin^2β (since cos(α-β)*cos(α+β)=cos^2α-sin^2β)
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