The value of 36(4 cos^2 9^{circ}-1)(4 cos^2 2 | vedclass

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(D) Using the identity $4 \cos^2 	heta - 1 = \frac{\sin 3	heta}{\sin 	heta}$,we can simplify each term in the product.The expression becomes:$36

Vedclass · Accepted Answer

$36$

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(D) Using the identity $4 \cos^2 	heta - 1 = \frac{\sin 3	heta}{\sin 	heta}$,we can simplify each term in the product.The expression becomes:$36 	imes \left( \frac{\sin 27^{\circ}}{\sin 9^{\circ}} ight) 	imes \left( \frac{\sin 81^{\circ}}{\sin 27^{\circ}} ight) 	imes \left( \frac{\sin 243^{\circ}}{\sin 81^{\circ}} ight) 	imes \left( \frac{\sin 729^{\circ}}{\sin 243^{\circ}} ight)$Canceling the common terms in the numerator and denominator,we get:$36 	imes \frac{\sin 729^{\circ}}{\sin 9^{\circ}}$Since $\sin 729^{\circ} = \sin(2 	imes 360^{\circ} + 9^{\circ}) = \sin 9^{\circ}$,the expression simplifies to:$36 	imes \frac{\sin 9^{\circ}}{\sin 9^{\circ}} = 36$

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

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