MCQ
$\sin 4 \theta$ can be written as
  • $4 \sin \theta\left(1-2 \sin ^2 \theta\right) \sqrt{1-\sin ^2 \theta}$
  • B
    $2 \sin \theta \cos \theta \sin ^2 \theta$
  • C
    $4 \sin \theta-6 \sin ^3 \theta$
  • D
    $4 \sin \theta+6 \sin ^2 \theta$

Answer

Correct option: A.
$4 \sin \theta\left(1-2 \sin ^2 \theta\right) \sqrt{1-\sin ^2 \theta}$
(A)
$\sin 4 \theta=2 \sin 2 \theta \cos 2 \theta$
$=2.2 \sin \theta \cos \theta\left(1-2 \sin ^2 \theta\right)$
$=4 \sin \theta\left(1-2 \sin ^2 \theta\right) \sqrt{1-\sin ^2 \theta}$

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