दिया है -
$cos (alpha-beta)+cos(beta-gamma)+cos(gamma-alpha)=-(3)/(2)$
$rArr 2(cos alpha cos beta+sin alpha sin beta+cos beta cos gamma + sin beta sin gamma+cos gamma cos alpha+sin gamma sin alpha)+3=0$
$rArr 2[(cos alpha cos beta+cos beta cos gamma+cos gamma cos alpha)+(sin alpha sin beta+sin beta sin gamma +sin alpha)]+1+1+1=0$
$rArr 2[(cos alpha cos beta+cos beta cos gamma+cos gamma cos alpha)+(sin alpha sin beta+sin beta sin gamma +sin gamma sin alpha)]+(cos^(2)alpha+sin^(2)alpha)+(cos^(2) beta +sin^(2)beta)+(cos^(2)gamma +sin^(2)gamma)=0$
$rArr [cos^(2)alpha+cos^(2)beta+cos^(2)gamma +2(cos alphacos beta +cos beta cos gamma+cos gamma cos alpha)]+[(sin^(2)alpha+sin alpha)]=0$
$rArr(cos alpha+cos beta+cos gamma)^(2)+(sin alpha+sin beta +sin gamma)^(2)=0$
$rArr cos alpha +cos beta+gamma=0 " तथा "sin alpha +sin beta +singamma = 0" "$यही सिद्ध करना था ।
