The value of sin 10^circ sin 30^circ sin 50^c | vedclass

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Question

(D) We use the identity $\sin 	heta \sin(60^\circ - 	heta) \sin(60^\circ + 	heta) = \frac{1}{4} \sin 3	heta$.Given expression: $E = \sin 10^\circ

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$\frac{1}{16}$

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(D) We use the identity $\sin 	heta \sin(60^\circ - 	heta) \sin(60^\circ + 	heta) = \frac{1}{4} \sin 3	heta$.Given expression: $E = \sin 10^\circ \sin 30^\circ \sin 50^\circ \sin 70^\circ$.Rearranging the terms: $E = \sin 30^\circ [\sin 10^\circ \sin(60^\circ - 10^\circ) \sin(60^\circ + 10^\circ)]$.Using the identity with $	heta = 10^\circ$: $E = \sin 30^\circ [\frac{1}{4} \sin(3 	imes 10^\circ)]$.Since $\sin 30^\circ = \frac{1}{2}$,we have $E = \frac{1}{2} [\frac{1}{4} \sin 30^\circ]$.Substituting $\sin 30^\circ = \frac{1}{2}$ again: $E = \frac{1}{2} [\frac{1}{4} 	imes \frac{1}{2}] = \frac{1}{2} 	imes \frac{1}{8} = \frac{1}{16}$.

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

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