If $\sin 6\theta = 32{\cos ^5}\theta \sin \theta - 32{\cos ^3}\theta \sin \theta + 3x,$ then $x = $

  • A

    $\cos \theta $

  • B

    $\cos 2\theta $

  • C

    $\sin \theta $

  • D

    $\sin 2\theta $

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$\tan 20^\circ \tan 40^\circ \tan 60^\circ \tan 80^\circ = $

  • [IIT 1974]

The value of $cosec \frac{\pi }{{18}} - \sqrt 3 \,sec\, \frac{\pi }{{18}}$ is a