The number of solutions of the equation $1 + {\sin ^4}\,x = {\cos ^2}\,3x,x\,\in \,\left[ { - \frac{{5\pi }}{2},\frac{{5\pi }}{2}} \right]$ is

  • [JEE MAIN 2019]
  • A

    $3$

  • B

    $4$

  • C

    $5$

  • D

    $7$

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If $(2\cos x - 1)(3 + 2\cos x) = 0,\,0 \le x \le 2\pi $, then $x = $

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The value of the expression

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