In triangle ABC, prove that the maximum value of `tanA/2tanB/2tanC/2i s R/(2s)`

Explanation

`tan(A/2)tan(B/2)tan(C/2)`

`sqrt(((s-b)(s-c))/(s(s-a)))sqrt(((s-a)(s-c))/(s(s-b)))sqrt((s-a)(s-b))/(s(s-c)`

`sqrt((s(s-a)(s-b)(s-c))/s^4`

`/_/s^2=r/s<=R/(2s)`.