यदि k = sin frac{pi}{18} cdot sin frac{5pi}{1 | vedclass

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(B) दिया गया है $k = \sin \frac{\pi}{18} \sin \frac{5\pi}{18} \sin \frac{7\pi}{18}$.सर्वसमिका $\sin 	heta = \cos \left( \frac{\pi}{2} - 	heta ight

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$\frac{1}{8}$

Vedclass · Answer

(B) दिया गया है $k = \sin \frac{\pi}{18} \sin \frac{5\pi}{18} \sin \frac{7\pi}{18}$.सर्वसमिका $\sin 	heta = \cos \left( \frac{\pi}{2} - 	heta ight)$ का उपयोग करने पर:$k = \cos \left( \frac{\pi}{2} - \frac{\pi}{18} ight) \cos \left( \frac{\pi}{2} - \frac{5\pi}{18} ight) \cos \left( \frac{\pi}{2} - \frac{7\pi}{18} ight)$$k = \cos \frac{4\pi}{9} \cos \frac{2\pi}{9} \cos \frac{\pi}{9}$.सूत्र $\cos 	heta \cos 2	heta \cos 4	heta = \frac{\sin 8	heta}{8 \sin 	heta}$ का उपयोग करने पर,जहाँ $	heta = \frac{\pi}{9}$:$k = \frac{\sin \left( 8 \cdot \frac{\pi}{9} ight)}{8 \sin \frac{\pi}{9}} = \frac{\sin \frac{8\pi}{9}}{8 \sin \frac{\pi}{9}}$.चूँकि $\sin \frac{8\pi}{9} = \sin \left( \pi - \frac{\pi}{9} ight) = \sin \frac{\pi}{9}$:$k = \frac{\sin \frac{\pi}{9}}{8 \sin \frac{\pi}{9}} = \frac{1}{8}$.

यदि $k = \sin \frac{\pi}{18} \cdot \sin \frac{5\pi}{18} \cdot \sin \frac{7\pi}{18}$ है,तो $k$ का संख्यात्मक मान क्या है?

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