If $\cos ^3 80^{\circ}+\cos ^3 40^{\circ}-\cos ^3 20^{\circ}=\mathrm{k}$, then $\frac{4 \mathrm{k}}{3}=$

• A

  $\sin \left(\frac{4 \pi}{3}\right)$
• Correct answer
  B

  $\cos \left(\frac{2 \pi}{3}\right)$
• C

  $\tan \left(\frac{\pi}{3}\right)$
• D

  $\sec \left(\frac{2 \pi}{3}\right)$

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