In a `!ABC` , 2r = `r_(1)` and A=30 , then cos `(B - C)/2` is equal to

Options

A. `(3sqrt3)/(2sqrt2)`
B. `(3(sqrt3-1))/(2sqrt2)`
C. `(3(sqrt3-1))/(2sqrt3)`
D. none of these

Explanation

We have,
`2r=r_(1)`
`rArr(2Delta)/s=(Delta)/(s-a)`
`rArr2s-2a=s`
`rArrs=2a`
`rArra+b+c=4a`
`rArrb+c=3a`
`rArr(b+c)/a=3`
`rArr(sinB+sinC)/(sinA)=3`
`rArr(2sin(B+C)/2cos(B-C)/2)/(2sinA/2cosA/2)=3`
`rArrcos((B-C)/2)=3sinA/2`
`cos(B-C)/2=3sin15^(@)rArrcos(B-C)/2=3((sqrt3-1)/(2sqrt2))`