If sin α and cos α are the roots of the equation ax2 +bx+c=0, then
a2−b2+2ac=0
(a−c)2=b2+c2
a2+b2−2ac=0
a2+b2+2ac=0
. Since, sin α and cos α are the roots of the equation ax2+ bx+ c=0, then,sinα+cosα=−ba and sinαcosα=caTo eliminate α we have1=sin2α+cos2α⇒ 1=(sinα+cosα)2−2sinαcosα⇒ 1=b2a2−2ca⇒ a2−b2+2ac=0