In `DeltaABC`, prove that: `cot A/2+cot B/2+cot C/2=((a+b+c)^(2))/(4Delta)`

In `DeltaABC`, prove that: `cot A/2+cot B/2+cot C/2=((a+b+c)^(2))/(4De

1.	In `DeltaABC`, prove that: `cot A/2+cot B/2+cot C/2=((a+b+c)^(2))/(4Delta)`
Answer» LHS `=cotA/2+cotB/2+cotC/2` `=sqrt((s(s-a))/((s-b)(s-c))+sqrt((s(s-b))/((s-a)(s-c)) + sqrt((s(s-c))/((s-a)(s-b))` `=(sqrt(s)[(s-a)+(s-b)+(s-c)])/(sqrt((s-a)(s-b)(s-c)))` `(sqrt(s)[(s-a)+(s-b)+(s-c)])/(sqrt((s-a)(s-b)(s-c)))` `(sqrt(s).sqrt(s)[3s-(a+b+c)])/(sqrt(s)(s-a)(s-b)(s-c))` `(s.(3s-2s))/(Delta)=s^(2)/Delta=(4s^(2))/(4Delta)` `=(2s)^(2)/(4Delta)=(a+b+c)^(2)/(4Delta)`= RHS Hence Proved.