The value of frac{4 sin 9^{circ} sin 21^{circ | vedclass

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(C) Let $E = \frac{4 \sin 9^{\circ} \sin 21^{\circ} \sin 39^{\circ} \sin 51^{\circ} \sin 69^{\circ} \sin 81^{\circ}}{\sin 54^{\circ}}$.Using $\sin 	h

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$\frac{1}{8}$

Vedclass · Answer

(C) Let $E = \frac{4 \sin 9^{\circ} \sin 21^{\circ} \sin 39^{\circ} \sin 51^{\circ} \sin 69^{\circ} \sin 81^{\circ}}{\sin 54^{\circ}}$.Using $\sin 	heta \sin(60^{\circ}-	heta) \sin(60^{\circ}+	heta) = \frac{1}{4} \sin 3	heta$:Group the terms: $(\sin 9^{\circ} \sin 51^{\circ} \sin 69^{\circ}) = \sin 9^{\circ} \sin(60^{\circ}-9^{\circ}) \sin(60^{\circ}+9^{\circ}) = \frac{1}{4} \sin 27^{\circ}$.And $(\sin 21^{\circ} \sin 39^{\circ} \sin 81^{\circ}) = \sin 21^{\circ} \sin(60^{\circ}-21^{\circ}) \sin(60^{\circ}+21^{\circ}) = \frac{1}{4} \sin 63^{\circ}$.Substituting these into the expression:$E = \frac{4 \cdot (\frac{1}{4} \sin 27^{\circ}) \cdot (\frac{1}{4} \sin 63^{\circ})}{\sin 54^{\circ}}$$E = \frac{\frac{1}{4} \sin 27^{\circ} \cos 27^{\circ}}{\sin 54^{\circ}}$$E = \frac{\frac{1}{8} \sin 54^{\circ}}{\sin 54^{\circ}} = \frac{1}{8}$.

The value of $\frac{4 \sin 9^{\circ} \sin 21^{\circ} \sin 39^{\circ} \sin 51^{\circ} \sin 69^{\circ} \sin 81^{\circ}}{\sin 54^{\circ}}$ is equal to

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