cos frac{pi}{7} cos frac{2pi}{7} cos frac{3pi | vedclass

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(C) माना $P = \cos \frac{\pi}{7} \cos \frac{2\pi}{7} \cos \frac{3\pi}{7}$ है।$2 \sin \frac{\pi}{7}$ से गुणा और भाग करने पर:$P = \frac{1}{2 \sin \frac{

Vedclass · Accepted Answer

$\frac{1}{8}$

Vedclass · Answer

(C) माना $P = \cos \frac{\pi}{7} \cos \frac{2\pi}{7} \cos \frac{3\pi}{7}$ है।$2 \sin \frac{\pi}{7}$ से गुणा और भाग करने पर:$P = \frac{1}{2 \sin \frac{\pi}{7}} \left( 2 \sin \frac{\pi}{7} \cos \frac{\pi}{7} ight) \cos \frac{2\pi}{7} \cos \frac{3\pi}{7}$$2 \sin 	heta \cos 	heta = \sin 2	heta$ सूत्र का उपयोग करने पर:$P = \frac{1}{2 \sin \frac{\pi}{7}} \left( \sin \frac{2\pi}{7} \cos \frac{2\pi}{7} ight) \cos \frac{3\pi}{7}$$2$ से गुणा और भाग करने पर:$P = \frac{1}{4 \sin \frac{\pi}{7}} \left( 2 \sin \frac{2\pi}{7} \cos \frac{2\pi}{7} ight) \cos \frac{3\pi}{7} = \frac{1}{4 \sin \frac{\pi}{7}} \sin \frac{4\pi}{7} \cos \frac{3\pi}{7}$चूंकि $\sin \frac{4\pi}{7} = \sin \left( \pi - \frac{3\pi}{7} ight) = \sin \frac{3\pi}{7}$:$P = \frac{1}{4 \sin \frac{\pi}{7}} \sin \frac{3\pi}{7} \cos \frac{3\pi}{7}$$2$ से गुणा और भाग करने पर:$P = \frac{1}{8 \sin \frac{\pi}{7}} \left( 2 \sin \frac{3\pi}{7} \cos \frac{3\pi}{7} ight) = \frac{1}{8 \sin \frac{\pi}{7}} \sin \frac{6\pi}{7}$चूंकि $\sin \frac{6\pi}{7} = \sin \left( \pi - \frac{\pi}{7} ight) = \sin \frac{\pi}{7}$:$P = \frac{\sin \frac{\pi}{7}}{8 \sin \frac{\pi}{7}} = \frac{1}{8}$.

$\cos \frac{\pi}{7} \cos \frac{2\pi}{7} \cos \frac{3\pi}{7} =$

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