Prove that `(b^2+c^2)/(b+c)+(c^2+a^2)/(c+a)+(a^2+b^2)/(a+b)> a+b+c`

For any triangle ABC, prove that (b^2 c^2) cot"A"+"(c^2 a^2)"cot"B""+""(a^2 b^2)" cot"C" "="\ "0

If a,b and c are non- zero real number then 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 a ,b ,c in R^+ , then the minimum value of a(b^2+c^2)+b(c^2+a^2)+c(a^2+b^2) is equal to (a) a b c (b) 2a b c (c) 3a b c (d) 6a b c

In triangle ABC , a (b^2 +c^2 ) cos A + b (c^2 +a^2 ) cos B + c(a^2 +b^2 ) cos C is equal to

Prove that b^2c^2+c^2a^2+a^2b^2> a b cxx(a+b+c)(a ,b ,c >0) .

Prove that 2/(b+c)+2/(c+a)+2/(a+b) 0.

In any /_\ A B C , prove that (b^2-c^2)cotA+(c^2-a^2)cotB+(c^a-b^2)cotC=0

With usual notations, in triangle A B C ,acos(B-C)+bcos(C-A)+c"cos"(A-B) is equal to(a) (a b c)/R^2 (b) (a b c)/(4R^2) (c) (4a b c)/(R^2) (d) (a b c)/(2R^2)

In Delta ABC, prove that (a^(2) - b^(2) + c^(2)) tan B = (a^(2) + b^(2) - c^(2)) tan C.

Show that |{:( 2bc-a^2 , c^2 ,b^2),(c^2 , 2ca-b^2 , a^2),(b^2 , a^2 , 2ab-c^2):}| = |{:(a,b,c),(b,c,a),(c,a,b):}|^2