If a,b,c are in A.P. prove that `b+c,c+a,a+b ` are also in A.P.

If a,b,c are in A.P. prove that (i) b+c,c+a,a+b are also in A.P. (ii) 1/(sqrt(b)+sqrt(c)),1/(sqrt(c)+sqrt(a)),1/(sqrt(a)+sqrt(b)) are also in A.P.

If a,b,c are in A.P. then

If a,b,c are in AP , then prove that : b+c,c+a,a+b are also in AP

If (b+c)/(a),(c+a)/(b),(a+b)/(c) are in A.P.prove that :bc,ca,ab are in A.P.

If a^(2)(b+c),b^(2)(c+a),c^(2)(a+_b) are in in A.P. then prove that a, b, c, are also in A.P. or ab + bc + ca = 0.

In DeltaABC , a^(2),b^(2),c^(2) are in A.P. Prove that cotA, cotB, cotC are also in A.P.

If a,b,c are in G.P.prove that log a,log b,log c are in A.P.

If a,b,c are in A.P.then prove that the following are also in A.P.(1)/(sqrt(b)+sqrt(c)),(1)/(sqrt(c)+sqrt(a)),(1)/(sqrt(a)+sqrt(b))

if (1)/(b+c),(1)/(c+a),(1)/(a+b) are in A.P. prove that a^(2),b^(2),c^(2) are also in A.P.

If (b+c-a)/a,(c+a-b)/b,(a+b-c)/c are in A.P. Prove that 1/a,1/b,1/c are also inA.P