In triangle `A B C ,` if `cosA+cosB+cosC=7/4, t h e n R/r` is equal to `3/4` (b) `4/3` (c) `2/3` (d) `3/2`

Explanation

Here, we will use,

`cosA+cosB+cosC = 1+4sin(A/2)sin(B/2)sin(C/2)`

`cosA+cosB+cosC = 7/4`

`:. 1+4sin(A/2)sin(B/2)sin(C/2) = 7/4`

`=> 4sin(A/2)sin(B/2)sin(C/2) = 7/4-1`

`=> 4sin(A/2)sin(B/2)sin(C/2) = 3/4->(1)`

Now, `r = 4Rsin(A/2)sin(B/2)sin(C/2)`

`:. r/R = 4sin(A/2)sin(B/2)sin(C/2)->(2)`

...