Question

Find the value of $sin \frac{5\pi}{12}\,sin \, \frac{\pi}{12}$.

• A. $1/2$
• B. $1/4$
• C. $0$
• D. $1$

Answer 1

Answer: (B)

$1/4$

Answer 2

We have, $sin \frac{5\pi}{12}\cdot sin \frac{\pi}{12}=\frac{1}{2}\left[2\,sin \frac{5\pi}{12}\cdot sin \frac{\pi}{12}\right]$ $=\frac{1}{2}\left[cos\left(\frac{5\pi}{12}-\frac{\pi}{12}\right)-cos\left(\frac{5\pi}{12}+\frac{\pi}{12}\right)\right]$ $=\frac{1}{2}\left(cos \frac{\pi}{3}-cos \frac{\pi}{2}\right)=\frac{1}{2}\left[\frac{1}{2}-0\right]$ $=\frac{1}{4}$