If the cotangents of half the angles of a triangle are in A.P., then prove that the sides are in A.P.

Explanation

It is given that ,

`2cot (B/2) = cot (A/2)+cot(C/2)`

`=>2sqrt(((s(s-b)))/((s-a)(s-c))) = sqrt(((s(s-a)))/((s-b)(s-c)))+sqrt(((s(s-c)))/((s-a)(s-b)))`

`=>2sqrt((s(s-b)s(s-b))/(s(s-b)(s-a)(s-c))) = sqrt((s(s-a)s(s-a))/(s(s-b)(s-a)(s-c))) +sqrt((s(s-c)s(s-c))/(s(s-b)(s-a)(s-c))) `

`=>2s(s-b) = s(s-a)+s(s-c)`

`=>2(s-b) = s-a+s-c`

`=>2s-2b = s-a+s-c`

`=>2b = a+c`

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