Prove that three no's a,b,c are in AP ; If `2b=a+c`

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) and c^(2) be in A.P. prove that cot A,cot B and cot C are in A.P. also.

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

In a triangle A B C , if cos A+2\ cos B+cos C=2. prove that the sides of the triangle are in A.P.

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.

If a, b, c are in A.P. then show that 2b = a + c.

If a^(2),b^(2),c^(2) are in A.P.,then prove that the following are also in A.P.(i) (1)/(b+c),(1)/(c+a),(1)/(a+b) (ii) (a)/(b+c),(b)/(c+a),(c)/(a+b)

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