Question:

The value of $36(4\cos^2 9°-1)(4\cos^2 27°-1)(4\cos^2 81°-1)(4\cos^2 243°-1)$ is

Step-by-Step Solution

Key Concept: $4\cos^2\theta-1=(2\cos\theta-1)(2\cos\theta+1)$. Group pairs and use product-to-sum identities involving $\sin18°$ and $\sin54°$.

Product simplifies to $36$.

Correct Answer: 4