1.

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`

Answer» 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)`
From (1) and (2),
`r/R = 3/4`
`:. R/r = 4/3.`


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