The value of $\displaystyle\prod_{r=1}^{7} \cos\frac{r\pi}{15}$ is
Step-by-Step Solution
Key Concept: Group the product and use known results: $\prod_{r=1}^{n-1}\sin\frac{r\pi}{n}=\frac{n}{2^{n-1}}$. Alternatively group into subproducts with known values.
Product $= \frac{1}{16}\cdot\frac{1}{4}\cdot\frac{1}{2} = \frac{1}{128}$.
Correct Answer: (B) $\dfrac{1}{128}$