sin left( frac{pi}{10} right) sin left( frac{ | vedclass

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(C) We know that $\frac{\pi}{10} = 18^\circ$ and $\frac{3\pi}{10} = 54^\circ$.Thus,the expression is $\sin 18^\circ \sin 54^\circ$.We know that $\sin

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$1/4$

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(C) We know that $\frac{\pi}{10} = 18^\circ$ and $\frac{3\pi}{10} = 54^\circ$.Thus,the expression is $\sin 18^\circ \sin 54^\circ$.We know that $\sin 54^\circ = \cos(90^\circ - 54^\circ) = \cos 36^\circ$.Using the standard values: $\sin 18^\circ = \frac{\sqrt{5} - 1}{4}$ and $\cos 36^\circ = \frac{\sqrt{5} + 1}{4}$.Multiplying these values: $\left( \frac{\sqrt{5} - 1}{4} \right) \left( \frac{\sqrt{5} + 1}{4} \right) = \frac{(\sqrt{5})^2 - 1^2}{16} = \frac{5 - 1}{16} = \frac{4}{16} = \frac{1}{4}$.

$\sin \left( \frac{\pi}{10} \right) \sin \left( \frac{3\pi}{10} \right) = $

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