In `a DeltaABC, cos""(A)/(2)cos""(B)/(2)cos""C/(2)` is

Options

A. `le(3sqrt3)/(16)`
B. `le(3sqrt3)/(8)`
C. `le(3sqrt3)/(32)`
D. `(3sqrt3)/(64)`

Answer

B

Explanation

We know that
`cosA+cosB+cosCle(3)/(2)`
`implies(1+cosA)+(1+cosB)+(1+cosC)le9/2`
`impliescos^(2)""(A)/(2)+cos^(2)""(B)/(2)+cos^(2)""(C)/(2)le9/4`
`implies3/4ge(cos^(2)""(A)/(2)+cos^(2)""(B)/(2)+cos^(2)""(C)/(2))/(3)ge(cos^(2)""(A)/(2)cos^(2)""(B)/(2)cos^(2)""(C)/(2))^(1//3)`
`implies((3)/(4))^(3//2)gecos""(A)/(2)c os""(B)/(2)cos""(C)/(2)`