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If A + B + C = pi/3 then sin ( (pi-6A)...

If A + B + C = `pi/3` then
`sin ( (pi-6A)/(6) ) + sin ( (pi -6B)/(6) )+sin C = `

A

A. `- 1 + 4 cos ( (pi - 6A)/(6) ) + cos ( (pi - 6B)/(12) ) + sin C/2`

B

B. `4 sin ( (pi + 6A )/(12 ) ) sin ( (pi + 6B)/(12) ) cos C/2`

C

C. `1 - 4 cos ( (pi - 6A)/(12) ) cos ( (pi - 6B)/(12) ) cos (pi - 6C)/(12)`

D

D. `4 cos ( (pi - 6A)/(12) ) cos ( (pi - 6B)/(12) ) sin C/2`

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The correct Answer is:
D
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