8 x 8 x 2 x 4 x 8 is equal to - Vidyadip

MCQ

$8 \sin \frac{x}{8} \cos \frac{x}{2} \cos \frac{x}{4} \cos \frac{x}{8}$ is equal to

A
$8 sin x$
✓
$sin x$
C
$cos x$
D
$8 cos x$

✓

Answer

Correct option: B.

$sin x$

(B)
$8 \sin \frac{x}{8} \cos \frac{x}{2} \cos \frac{x}{4} \cos \frac{x}{8}$
$=4\left(2 \sin \frac{x}{8} \cos \frac{x}{8}\right) \cos \frac{x}{2} \cos \frac{x}{4}$
$=4\left(\sin \frac{x}{4} \cos \frac{x}{2} \cos \frac{x}{4}\right)$
$\ldots[\because 2 \sin A \cos A=\sin 2 A]$
$=2\left(2 \sin \frac{x}{4} \cos \frac{x}{4}\right) \cos \frac{x}{2}$
$=2 \sin \frac{x}{2} \cos \frac{x}{2}=\sin x$

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