If $L=\sin ^{2}\left(\frac{\pi}{16}\right)-\sin ^{2}\left(\frac{\pi}{8}\right)$ and $M=\cos ^{2}\left(\frac{\pi}{16}\right)-\sin ^{2}\left(\frac{\pi}{8}\right),$ then 

  • [JEE MAIN 2020]
  • A

    $M =\frac{1}{2 \sqrt{2}}+\frac{1}{2} \cos \frac{\pi}{8}$

  • B

    $L =\frac{1}{4 \sqrt{2}}-\frac{1}{4} \cos \frac{\pi}{8}$

  • C

    $M =\frac{1}{4 \sqrt{2}}+\frac{1}{4} \cos \frac{\pi}{8}$

  • D

    $L =-\frac{1}{2 \sqrt{2}}+\frac{1}{2} \cos \frac{\pi}{8}$

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