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

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Question

(C) ધારો કે $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} \s

Vedclass · Accepted Answer

$\frac{1}{64}$

Vedclass · Answer

(C) ધારો કે $P = \sin \frac{\pi}{14} \sin \frac{3 \pi}{14} \sin \frac{5 \pi}{14} \sin \frac{7 \pi}{14} \sin \frac{9 \pi}{14} \sin \frac{11 \pi}{14} \sin \frac{13 \pi}{14}$.$\sin \frac{13 \pi}{14} = \sin \frac{\pi}{14}$,$\sin \frac{11 \pi}{14} = \sin \frac{3 \pi}{14}$,$\sin \frac{9 \pi}{14} = \sin \frac{5 \pi}{14}$ અને $\sin \frac{7 \pi}{14} = 1$ હોવાથી:$P = (\sin \frac{\pi}{14} \sin \frac{3 \pi}{14} \sin \frac{5 \pi}{14})^2 	imes 1$.$\sin 	heta = \cos (\frac{\pi}{2} - 	heta)$ નો ઉપયોગ કરતા:$P = (\cos \frac{3 \pi}{7} \cos \frac{2 \pi}{7} \cos \frac{\pi}{7})^2$.આપેલ નિત્યસમ મુજબ,$\cos \frac{\pi}{7} \cos \frac{2 \pi}{7} \cos \frac{4 \pi}{7} = -\frac{1}{8}$.તેથી,$P = (-\frac{1}{8})^2 = \frac{1}{64}$.

જો $\cos \frac{\pi}{7} \cos \frac{2 \pi}{7} \cos \frac{4 \pi}{7} = \frac{\sin \frac{8 \pi}{7}}{8 \sin \frac{\pi}{7}}$ હોય,તો $\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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