Question:

If $x=\cos1°\cos2°\cos3°\cdots\cos89°$ and $y=\cos2°\cos6°\cos10°\cdots\cos86°$, then $\dfrac{2}{7}\log_2\!\left(\dfrac{y}{x}\right)$ is equal to

Step-by-Step Solution

Key Concept: $x=\cos1°\cdots\cos89°$. Use the identity $\prod_{k=1}^{n-1}\sin(k\pi/n)=n/2^{n-1}$ to simplify.

$(2/7)\log_2(y/x)=19$.

Correct Answer: 1