$\cos ^3 \frac{\pi}{8} \cos \frac{3 \pi}{8}+\sin ^3 \frac{\pi}{8} \sin \frac{3 \pi}{8}=$

• Correct answer
  A

  $\frac{1}{2 \sqrt{2}}$
• B

  $\frac{1}{2}$
• C

  $\frac{1}{\sqrt{2}}$
• D

  $\frac{1}{4}$

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