$\alpha=\sin 36^{\circ}$ is a root of which of the following equation

  • [JEE MAIN 2022]
  • A

    $10 x^{4}-10 x^{2}-5=0$

  • B

    $16 x^{4}+20 x^{2}-5=0$

  • C

    $16 x^{4}-20 x^{2}+5=0$

  • D

    $16 x^{4}-10 x^{2}+5=0$

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  • [JEE MAIN 2023]

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$\frac{{\left (sin 36^o + cos 36^o - \sqrt 2  sin 27^o)( {\sin {{36}^0} + \cos {{36}^0} - \sqrt 2 \sin {{27}^0}} \right)}}{{2\sin {{54}^0}}}$ is less than