Value of frac{{4sin {9^o}sin {{21}^o}sin {{39 | vedclass

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Question

$\frac{4 \sin 9^{\circ} \sin 21^{\circ} \sin 39^{\circ} \sin 51^{\circ} \sin 69^{\circ} \sin 81^{\circ}}{\sin 54^{\circ}}$

$=\frac{4 \sin 9^{\circ}

Vedclass · Accepted Answer

$\frac{1}{8}$

Vedclass · Answer

$\frac{4 \sin 9^{\circ} \sin 21^{\circ} \sin 39^{\circ} \sin 51^{\circ} \sin 69^{\circ} \sin 81^{\circ}}{\sin 54^{\circ}}$

$=\frac{4 \sin 9^{\circ} \cos 9^{\circ} \cdot \sin 39^{\circ} \cos 39^{\circ} \sin 21^{\circ} \cos 21^{\circ}}{\sin 54^{\circ}}$

$=\frac{\sin 18^{\circ} \cdot \sin 78^{\circ} \sin 42^{\circ}}{2 \sin 54^{\circ}}$

$=\frac{\sin 18^{\circ}}{4} \frac{\left(\cos 36^{\circ}+\cos 60^{\circ}\right)}{\sin 54^{\circ}}=\frac{1}{8}$

Value of $\frac{{4\sin {9^o}\sin {{21}^o}\sin {{39}^o}\sin {{51}^o}\sin {{69}^o}\sin {{81}^o}}}{{\sin {{54}^o}}}$ is equal to

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