sin 10^{circ} cdot sin 30^{circ} cdot sin 50^ | vedclass

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Question

(D) આપણે જાણીએ છીએ કે $\sin 30^{\circ} = \frac{1}{2}$.ધારો કે $E = \sin 10^{\circ} \cdot \sin 30^{\circ} \cdot \sin 50^{\circ} \cdot \sin 70^{\circ}$.

Vedclass · Accepted Answer

$\frac{1}{16}$

Vedclass · Answer

(D) આપણે જાણીએ છીએ કે $\sin 30^{\circ} = \frac{1}{2}$.ધારો કે $E = \sin 10^{\circ} \cdot \sin 30^{\circ} \cdot \sin 50^{\circ} \cdot \sin 70^{\circ}$.$E = \frac{1}{2} \cdot (\sin 10^{\circ} \cdot \sin 50^{\circ} \cdot \sin 70^{\circ})$.નિત્યસમ $\sin 	heta \cdot \sin(60^{\circ}-	heta) \cdot \sin(60^{\circ}+	heta) = \frac{1}{4} \sin 3	heta$ નો ઉપયોગ કરતા,જ્યાં $	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}$.તેથી,$E = \frac{1}{2} \cdot \frac{1}{8} = \frac{1}{16}$.

$\sin 10^{\circ} \cdot \sin 30^{\circ} \cdot \sin 50^{\circ} \cdot \sin 70^{\circ}$ નું મૂલ્ય શું છે?

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