The value of cos frac{pi}{10} cos frac{2pi}{1 | vedclass

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(C) Let $	heta = \frac{\pi}{10}$. The expression is $E = \cos 	heta \cos 2	heta \cos 4	heta \cos 8	heta \cos 16	heta$.Using the formula $\cos

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$\frac{\cos(\pi/10)}{16}$

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(C) Let $	heta = \frac{\pi}{10}$. The expression is $E = \cos 	heta \cos 2	heta \cos 4	heta \cos 8	heta \cos 16	heta$.Using the formula $\cos 	heta \cos 2	heta \cos 4	heta \dots \cos 2^{n-1}	heta = \frac{\sin(2^n 	heta)}{2^n \sin 	heta}$,we have $n=5$.$E = \frac{\sin(2^5 	heta)}{2^5 \sin 	heta} = \frac{\sin(32 	heta)}{32 \sin 	heta}$.Since $	heta = \frac{\pi}{10}$,$32	heta = \frac{32\pi}{10} = 3\pi + \frac{2\pi}{10} = 3\pi + \frac{\pi}{5}$.$E = \frac{\sin(3\pi + \pi/5)}{32 \sin(\pi/10)} = \frac{-\sin(\pi/5)}{32 \sin(\pi/10)}$.Using $\sin(2A) = 2 \sin A \cos A$,we get $\sin(\pi/5) = 2 \sin(\pi/10) \cos(\pi/10)$.$E = \frac{-2 \sin(\pi/10) \cos(\pi/10)}{32 \sin(\pi/10)} = -\frac{1}{16} \cos(\pi/10)$.

The value of $\cos \frac{\pi}{10} \cos \frac{2\pi}{10} \cos \frac{4\pi}{10} \cos \frac{8\pi}{10} \cos \frac{16\pi}{10}$ is:

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