The value of $ \cos ^{3}\left(\frac{\pi}{8}\right) \cdot \cos \left(\frac{3 \pi}{8}\right)+\sin ^{3}\left(\frac{\pi}{8}\right) \cdot \sin \left(\frac{3 \pi}{8}\right)$ is 

  • [JEE MAIN 2020]
  • A

    $\frac{1}{4}$

  • B

    $\frac{1}{\sqrt{2}}$

  • C

    $\frac{1}{2\sqrt{2}}$

  • D

    $\frac{1}{2}$

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