Question

If $8\sin \theta \cos \theta \cos 2\theta \cos 4\theta =\sin x$, then $x=$

• A. $16\theta$
• B. $8\theta$
• C. $4\theta$
• D. $32\theta$

Answer 1

The correct option is B $8\theta$

$8\sin \theta \cos \theta \cos 2\theta \cos 4\theta =2\left[2\right(2\sin \theta \cos \theta \left)\cos 2\theta \right]\cos 4\theta =2\left[2\sin 2\theta \cos 2\theta \right]\cos 4\theta =2\sin 4\theta \cos 4\theta =\sin 8\theta \therefore x=8\theta$