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)

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