` Delta ABC ` में , ` cot ""( A)/(2) +cot ""( B)/(2) +cot ""(C)/(2) ` का मान है

Options

A. ` ((a+ b+c)/( b+c-a) ) cot ""(A)/(2) `
B. ` cot ""(A)/(2) `
C. ` (a+b+c)/( b+c-a)`
D. इनमें से कोई नहीं

Answer

A

Explanation

` cot ""( A)/(2) +cot ""( B)/(2) +cot ""(C)/(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)^ 2)/ ((s-a)(s-b)(s-c))) `

`" "+ sqrt ((s(s-b)^ 2)/ ((s-a)(s-b)(s-c))) `

`" "+ sqrt ((s(s-c)^ 2)/ ((s-a)(s-b)(s-c)))`

`= (sqrt s [(s-a)+(s-b)+(s-c)])/ (sqrt( (s-a)(s-b)(s-c)))`

` = (sqrt s [3s-(a+b+c)])/( sqrt ((s-a)(s-b)(s-c)))`

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

`" "xx (sqrt (s-a))/ (sqrt (s-a))`

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

`= (2s)/ (2s-2a) cot"" A/ 2 `

`= (a+b+c) /(b+c-a) cot"" A/ 2`