If $\mathrm{A}+\mathrm{B}+\mathrm{C}=4 \mathrm{~S}$ then $\sin (2 \mathrm{~S}-\mathrm{A})+\sin (2 \mathrm{~S}-\mathrm{B})+\sin (2 \mathrm{~S}-\mathrm{C})-\sin 2 \mathrm{~S}=$

• A

  $4 \cos \frac{\mathrm{~A}}{2} \cos \frac{\mathrm{~B}}{2} \cos \frac{\mathrm{C}}{2}$
• B

  $4 \sin \frac{\mathrm{~A}}{2} \cos \frac{\mathrm{~B}}{2} \cos \frac{\mathrm{C}}{2}$
• C

  $4 \cos \frac{\mathrm{~A}}{2} \sin \frac{\mathrm{~B}}{2} \cos \frac{\mathrm{C}}{2}$
• Correct answer
  D

  $4 \sin \frac{\mathrm{~A}}{2} \sin \frac{\mathrm{~B}}{2} \sin \frac{\mathrm{C}}{2}$

Hence, the correct answer is option: 'D'.