The value of sin 10^{circ} cdot sin 30^{circ} | vedclass

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(D) We know that $\sin 30^{\circ} = \frac{1}{2}$.Let $E = \sin 10^{\circ} \cdot \sin 30^{\circ} \cdot \sin 50^{\circ} \cdot \sin 70^{\circ}$.$E = \fra

Vedclass · Accepted Answer

$\frac{1}{16}$

Vedclass · Answer

(D) We know that $\sin 30^{\circ} = \frac{1}{2}$.Let $E = \sin 10^{\circ} \cdot \sin 30^{\circ} \cdot \sin 50^{\circ} \cdot \sin 70^{\circ}$.$E = \frac{1}{2} \cdot (\sin 10^{\circ} \cdot \sin 50^{\circ} \cdot \sin 70^{\circ})$.Using the identity $\sin 	heta \cdot \sin(60^{\circ}-	heta) \cdot \sin(60^{\circ}+	heta) = \frac{1}{4} \sin 3	heta$,where $	heta = 10^{\circ}$:$\sin 10^{\circ} \cdot \sin 50^{\circ} \cdot \sin 70^{\circ} = \sin 10^{\circ} \cdot \sin(60^{\circ}-10^{\circ}) \cdot \sin(60^{\circ}+10^{\circ}) = \frac{1}{4} \sin(3 	imes 10^{\circ}) = \frac{1}{4} \sin 30^{\circ} = \frac{1}{4} \cdot \frac{1}{2} = \frac{1}{8}$.Therefore,$E = \frac{1}{2} \cdot \frac{1}{8} = \frac{1}{16}$.

The value of $\sin 10^{\circ} \cdot \sin 30^{\circ} \cdot \sin 50^{\circ} \cdot \sin 70^{\circ}$ is

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