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 in A.P.

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

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

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

If a^2, b^2,c^2 are in A.P., then prove that tanA ,tanB ,tanC are in H.P.

If a ,b ,c in R+ form an A.P., then prove that a+1//(b c),b+1//(a c),c+1//(a b) are also in A.P.

If a, b, c are in A.P. then show that 3^(a), 3^(b), 3^(c) are in G.P.

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

If a ,b ,c are in A.P., then prove that the following are also in A.P. a^2(b+c),b^2(c+a),c^2(a+b)

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 l n(a+c),l n(a-c)a n dl n(a-2b+c) are in A.P., then (a) a ,b ,c are in A.P. (b) a^2,b^2, c^2, are in A.P. (c) a ,b ,c are in G.P. d. (d) a ,b ,c are in H.P.