If in a triangle `A B C ,(1+cosA)/a+(1+cosB)/b+(1_(cosC))/c` `=(k^2(1+cosA)(1+cosB)(1+cosC)/(a b c)` , then `k` is equal to `1/(2sqrt(2)R)` (b) `2R` (c) `1/R` (d) none of these

Explanation

`sinx/a=cosx/b=tanx/c=k`

`bc+1/(ek)+(ak)/(1+bk)`

`cosx/k*tanx/k+1/tanx+sinx/(1+cosx)`

`sinx/k^2+1/tanx+sinx/(1+cosx)`

`(ak)/k^2+(cos(1+cosx)+sin^2x)/(sinx(1+cosx)`

`a/k+1/sinx`

`a/k+1/(ak)`

`1/k[a+1/a]`.