8 sin

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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