In triangle ABC, if `A - B = 120^(2) and R = 8r`, where R and r have their usual meaning, then cos C equals

Options

A. `3//4`
B. `2//3`
C. `5//6`
D. `7//8`

Answer

D

Explanation

`R = 8r = 8 (4R sin.(A)/(2) sin.(B)/(2) sin.(C)/(2))`
`:. 2 sin.(A)/(2) sin.(B)/(2) sin.(C)/(2) = (1)/(16)`
or `(cos.(A -B)/(2) -cos.(A +B)/(2)) sin.(C)/(2) = (1)/(16)`
or `sin.(C)/(2) ((1)/(2) - sin.(C)/(2)) = (1)/(16) rArr sin.(C)/(2) = (1)/(4)`
or `cos C = 1 -2 sin^(2).(C)/(2) = 1 - (1)/(8) = (7)/(8)`