Question:
$8 \sin \frac{x}{8} \cos \frac{x}{2} \cos \frac{x}{4} \cos \frac{x}{8}$ is equal to
(a) 8 cos x
(b) cos x
(c) 8 sin x
(d) sin x
Solution:
(d) sin x
We have, $8 \sin \frac{x}{8} \cos \frac{x}{2} \cos \frac{x}{4} \cos \frac{x}{8}$
$=4 \times\left(2 \sin \frac{x}{8} \cos \frac{x}{8}\right) \cos \frac{x}{2} \cos \frac{x}{4}$
$=4 \times \sin \frac{x}{4} \cos \frac{x}{2} \cos \frac{x}{4}$
$=2 \times\left(2 \sin \frac{x}{4} \cos \frac{x}{4}\right) \cos \frac{x}{2}$
$=2 \times \sin \frac{x}{2} \cos \frac{x}{2}$
$=\sin x$
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