Question

The value of
$cos^{3}\left(\frac{\pi}{8}\right)\cdot cos \left(\frac{3\pi}{8}\right)+sin^{3}\left(\frac{\pi}{8}\right)\cdot sin \left(\frac{3\pi}{8}\right)$
is :

• A. $\frac{1}{4}$
• B. $\frac{1}{2\sqrt{2}}$
• C. $\frac{1}{2}$
• D. $\frac{1}{\sqrt{2}}$

Answer 1

Answer: (B)

$cos^{3}\frac{\pi}{8}\cdot sin\frac{\pi}{8}\cdot sin^{3} \frac{\pi}{8}. cos \frac{\pi}{8}$
$=sin \frac{\pi}{8}. cos \frac{\pi }{8}=\frac{1}{2}sin \frac{\pi}{4}=\frac{1}{2\sqrt{2}}$