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The value of $81 (4 \cos^{2} 9^{o} - 1) (4 \cos^{2} 27^{o} - 1)$ $(4 \cos^{2} 81^{o} - 1) (4 \cos^{2} 243^{o} - 1)$

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answer is B.

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Detailed Solution

$\frac{\sin 3 θ}{\sin θ} = 4 \cos^{2} θ - 1$

$∴$ given

$= 81 [\frac{\sin 27^{o}}{\sin 9^{o}} \times \frac{\sin 81^{o}}{\sin 27^{o}} \times \frac{\sin 243^{o}}{\sin 81^{o}} \times \frac{\sin 729^{o}}{\sin 243^{o}}]$

$= 81 [\frac{\sin 729^{o}}{\sin 9^{o}}] = 81 [\frac{\sin 9^{o}}{\sin 9^{o}}] = 81$

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