In triangle ABC, if `A - B = 120 and R = 8r`, where R and r have their usual meaning, then cos C equals

Explanation

`R = 8r`

`=>R = 8(4Rsin(A/2)sin(B/2)sin(C/2))`

`=>2sin(A/2)sin(B/2)sin(C/2) = 1/16`

`=>(cos((A-B)/2) - cos((A+B)/2))sinC/2 = 1/16`

As, `(A-B) = 120^@ and C = pi-(A+B),`

so, our equation becomes,

`=>(1/2-sin(C/2)) sin(C/2) = 1/16`

`=>sin(C/2) = 1/4`

...