Question

Find the value of `(4cos^(2)9^(@)-1)(4cos^(2)27^(@)-1)`
`(4cos^(2)81^(@)-1)(4cos^(2)243^(@)-1)`.

Answer 1

Correct Answer - 1
We have `cos^(2)theta-1=3-4sin^(2)theta=(sin 3theta)/(sin theta)`
`therefore` Given expression.
`=(4 cos^(2)theta-1)(4cos ^(2)3theta-1)(4cos^(2)9theta-1)(4cos^(2)27theta-1)`.
Where `theta=9^(@)`
`=(sin 3theta)/(sin theta)(sin 9thetA)/(sin 3theta)(sin 27theta)/(sin 9theta)(sin 81theta)/(sin 27theta)`
`=(sin 81theta)/(sin theta)=(sin 729^(@))/(sin9^(@))=1`