solve`(b^2-c^2)cotA+(c^2-a^2)cotB+(a^2-b^2)cotC=0`

In any DeltaABC , prove that (b^(2)-c^(2))cotA+(c^(2)+a^(2))cotB+(a^(2)-b^(2))cotC=0 .

In DeltaABC , (b-c)cotA/2+(c-a)cotB/2+(a-b)cotC/2=?

(b^(2)-c^(2))/(a)cos A+(c^(2)-a^(2))/(b)cos B+(a^(2)-b^(2))/(c)cos C=0

Prove: |(0,b^2a, c^2a),( a^2b,0,c^2b),( a^2c, b^2c,0)|=2a^3b^3c^3

Prove that : |{:(b^(2)c^(2),bc, b+c),(c^(2)a^(2),ca, c+a),(a^(2)b^(2),ab, a+b):}|=0

If sinthetaand costheta are the roots of the equation ax^2+bx+c=0 , then (A) (a-c)^2=b^2+c^2 (B) (a+c)^2=b^2-c^2 (C) a^2=b^2-2ac (D) a^2+b^2-2ac=0

If ab+bc+ca=0, then solve a(b-2c)x^(2)+b(c-2a)x+c(a-2b)=0

If (b^2+c^2-a^2)/(2b c),(c^2+a^2-b^2)/(2c a),(a^2+b^2-c^2)/(2a b) are in A.P. and a+b+c=0 then prove that a(b+c-a),b(c+a-b),c(a+b-c) are in A.P.

Prove that b^(2)c^(2)+c^(2)a^(2)+a^(2)+b^(2)>abc xx(a+b+c)(a,b,c>0)