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

Answer 1

(d) sin x

$$\begin{gathered} \mathrm{We}\mathrm{have},8\sin \frac{x}{8}\cos \frac{x}{2}\cos \frac{x}{4}\cos \frac{x}{8} \\ =4\times \left(2\sin \frac{x}{8}\cos \frac{x}{8}\right)\cos \frac{x}{2}\cos \frac{x}{4} \\ =4\times \sin \frac{x}{4}\cos \frac{x}{2}\cos \frac{x}{4} \\ =2\times \left(2\sin \frac{x}{4}\cos \frac{x}{4}\right)\cos \frac{x}{2} \\ =2\times \sin \frac{x}{2}\cos \frac{x}{2} \\ =\sin x \end{gathered}$$