If `a >0,b >0` and `c >0` prove that (1984, 2M) `(a+b+c)(1/a+1/b+1/c)geq9`

If a > b > c >0 , prove that cot^(-1)((a b+1)/(a-b))+cot^(-1)((b c+1)/(b-c))+cot^(-1)((c a+1)/(c-a))=pi

If a>0,b>0,c>0 prove that a/(b+c)+b/(c+a)+c/(a+b)ge3/2 .

If a+b+c=1 and a>0,b>0,c>0 then prove that ab^2c^3le1/(432) .

If a,b,c are real numbers such that 0 lt a lt 1, 0 lt b gt 1, 0 lt c lt 1, a + b + c = 2 , then prove that (a)/(1 - a) (b)/(1 - b) (c )/(1 - c) ge 8 .

If (a)/(b+c),(b)/(c+a),(c)/(a+b) are in A.P.and a+b+c!=0 prove that (1)/(b+c),(1)/(c+a),(1)/(a+b) are in A.P.

prove that det[[1,a,b+c1,b,c+a1,c,a+b]]=0

Prove that: |1a a^2-b c1bb^2-c a1cc^2-a b|=0

If a ,b ,c in R^+t h e n(a+b+c)(1/a+1/b+1/c) is always (a)geq12 (b)geq9 (c)lt=12 (d)none of these