96 cos frac{pi}{33} cos frac{2 pi}{33} cos fr | vedclass

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Question

(A) Let $P = 96 \cos \frac{\pi}{33} \cos \frac{2 \pi}{33} \cos \frac{4 \pi}{33} \cos \frac{8 \pi}{33} \cos \frac{16 \pi}{33}$.Using the formula $\cos

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(A) Let $P = 96 \cos \frac{\pi}{33} \cos \frac{2 \pi}{33} \cos \frac{4 \pi}{33} \cos \frac{8 \pi}{33} \cos \frac{16 \pi}{33}$.Using the formula $\cos 	heta \cos 2	heta \cos 4	heta \dots \cos 2^{n-1}	heta = \frac{\sin(2^n 	heta)}{2^n \sin 	heta}$,where $n=5$ and $	heta = \frac{\pi}{33}$.$P = 96 	imes \frac{\sin(2^5 	imes \frac{\pi}{33})}{2^5 \sin \frac{\pi}{33}}$$P = 96 	imes \frac{\sin \frac{32 \pi}{33}}{32 \sin \frac{\pi}{33}}$Since $\sin \frac{32 \pi}{33} = \sin(\pi - \frac{\pi}{33}) = \sin \frac{\pi}{33}$,we have:$P = \frac{96}{32} 	imes \frac{\sin \frac{\pi}{33}}{\sin \frac{\pi}{33}}$$P = 3 	imes 1 = 3$.

$96 \cos \frac{\pi}{33} \cos \frac{2 \pi}{33} \cos \frac{4 \pi}{33} \cos \frac{8 \pi}{33} \cos \frac{16 \pi}{33}$ is equal to $......$.

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