Question

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

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

Answer 1

Answer: (B)

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