If `(a-c)^2,(c-a)^2,(a-b)^2` are in A.P.,prove that `1/(b-c),1/(c-a),1/(a-b)` are in A.P.

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

If (b+c)/a,(c+a)/b,(a+b)/c are in A.P.,prove that 1/a,1/b,1/c are in A.P. given a+b+cne0.

If 1/a,1/b,1/c are in A.P. and a+b+cne0_2 prove that (b+c)/a,(c+a)/b,(a+b)/c are in A.P.

If a^2,b^2,c^2 being A.P prove that cotA,cotB,cotC are also In A.P.

If the side lengths a,b and c are in A.P. prove that cot (A/2),cot (B/2),cot (C/2) are in A.P .

If a,b,c,d are in G.P., prove that (a^2+b^2+c^2)(b^2+c^2+d^2)=(ab+bc+cd)^2.

If sinA : sinC = sin(A-B): sin(B-C) prove that a^2,b^2,c^2 are in A.P.

If a,b,c are respectively the p^(th),q^(th),r^(th) terms of an A.P.,then prove that a(q-r)+b(r-p)+c(p-q)=0