यदि cos frac{pi}{7} cos frac{2 pi}{7} cos fra | vedclass

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Question

(C) माना $P = \sin \frac{\pi}{14} \sin \frac{3 \pi}{14} \sin \frac{5 \pi}{14} \sin \frac{7 \pi}{14} \sin \frac{9 \pi}{14} \sin \frac{11 \pi}{14} \sin

Vedclass · Accepted Answer

$\frac{1}{64}$

Vedclass · Answer

(C) माना $P = \sin \frac{\pi}{14} \sin \frac{3 \pi}{14} \sin \frac{5 \pi}{14} \sin \frac{7 \pi}{14} \sin \frac{9 \pi}{14} \sin \frac{11 \pi}{14} \sin \frac{13 \pi}{14}$ है।चूंकि $\sin \frac{13 \pi}{14} = \sin \frac{\pi}{14}$,$\sin \frac{11 \pi}{14} = \sin \frac{3 \pi}{14}$,$\sin \frac{9 \pi}{14} = \sin \frac{5 \pi}{14}$ और $\sin \frac{7 \pi}{14} = 1$ है,इसलिए:$P = (\sin \frac{\pi}{14} \sin \frac{3 \pi}{14} \sin \frac{5 \pi}{14})^2 	imes 1$.$\sin 	heta = \cos (\frac{\pi}{2} - 	heta)$ का उपयोग करने पर:$P = (\cos \frac{3 \pi}{7} \cos \frac{2 \pi}{7} \cos \frac{\pi}{7})^2$.दिए गए सर्वसमिका के अनुसार,$\cos \frac{\pi}{7} \cos \frac{2 \pi}{7} \cos \frac{4 \pi}{7} = -\frac{1}{8}$ है।अतः,$P = (-\frac{1}{8})^2 = \frac{1}{64}$।

यदि $\cos \frac{\pi}{7} \cos \frac{2 \pi}{7} \cos \frac{4 \pi}{7} = \frac{\sin \frac{8 \pi}{7}}{8 \sin \frac{\pi}{7}}$ है,तो $\sin \frac{\pi}{14} \sin \frac{3 \pi}{14} \sin \frac{5 \pi}{14} \sin \frac{7 \pi}{14} \sin \frac{9 \pi}{14} \sin \frac{11 \pi}{14} \sin \frac{13 \pi}{14} = $

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