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

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.

If a^(2),b^(2),c^(2) are in A.P.then prove that cot A,cot B,cot C are in A.P.

If a^(2),b^(2),c^(2) are in A.P,then show that: b+c-a,c+a-b,a+b-c are in A.P.

"If "(1)/(a+b),(1)/(2b),(1)/(b+c) are in A.P., then prove that a, b, c are in G.P.

If a^(2),b^(2),c^(2) are in A.P. ,then show that b+c,c+a,a+b are in H.P.

If a^(2),b^(2),c^(2) are in A.P.prove that cot A,cot B,cot C are in A.P.

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

If a^(2),b^(2),c^(2) are in A.P.then show that: bc-a^(2),ca-b^(2),ab-c^(2) are in A.P.

If (b+c),(c+a),(a+b) are in H. P.then prove that (a)/(b+c),(b)/(c+a),(c)/(a+b) are in A.P