Question

The value of $(4co{s}^2{9}^o-1)(4co{s}^2{27}^o-1)(4co{s}^2{81}^o-1)(4co{s}^2{243}^o-1)$ is

• A. 1
• B. -1
• C. 2
• D. none of these

Answer 1

The correct option is A 1

As we know the derived formula for

$4co{s}^2\theta -1=\frac{sin3\theta }{sin\theta }$

Given expression,

$(4co{s}^2\theta -1)(4co{s}^{2}27\theta -1)(4co{s}^{2}81-1)(4co{s}^{2}243-1)$

Using above formula

we have

$\frac{sin27}{sin9}\times \frac{sin81}{sin27}\times \frac{sin243}{sin81}\times \frac{sin729}{sin243}=\frac{sin729}{sin9}=\frac{sin2\times 2\pi +9}{sin9}=\frac{sin9}{sin9}=1$