Question

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

• A. 8 cos x
• B. cos x
• C. 8 sin x
• D. sin x

Answer 1

The correct option is D

sin x

We have,

$8sin\frac{x}{8}cos\frac{x}{2}cos\frac{x}{4}cos\frac{x}{8}=4\times \left(2sin\frac{x}{8}cos\frac{x}{8}\right)cos\frac{x}{2}cos\frac{x}{4}=4\times sin\frac{x}{4}cos\frac{x}{2}cos\frac{x}{2}=2\times \left(2sin\frac{x}{4}cos\frac{x}{4}\right)cos\frac{x}{2}=2\times sin\frac{x}{2}cos\frac{x}{2}$
= sin x