If cos frac{pi}{4} cos frac{pi}{8} cos frac{p | vedclass

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(C) We use the formula $\prod_{k=1}^{n} \cos \frac{	heta}{2^k} = \frac{\sin 	heta}{2^n \sin(	heta/2^n)}$.Here,$	heta = \frac{\pi}{2}$ and $n=4$.So

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$28$

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(C) We use the formula $\prod_{k=1}^{n} \cos \frac{	heta}{2^k} = \frac{\sin 	heta}{2^n \sin(	heta/2^n)}$.Here,$	heta = \frac{\pi}{2}$ and $n=4$.So,$\cos \frac{\pi}{4} \cos \frac{\pi}{8} \cos \frac{\pi}{16} \cos \frac{\pi}{32} = \frac{\sin(\pi/2)}{2^4 \sin(\pi/32)} = \frac{1}{16 \sin(\pi/32)}$.This is equal to $\frac{1}{16} \operatorname{cosec} \frac{\pi}{32} = 2^{-4} \operatorname{cosec} \frac{\pi}{32}$.Comparing with $2^m \operatorname{cosec} \frac{\pi}{n}$,we get $m = -4$ and $n = 32$.Thus,$m+n = -4 + 32 = 28$.

If $\cos \frac{\pi}{4} \cos \frac{\pi}{8} \cos \frac{\pi}{16} \cos \frac{\pi}{32} = 2^m \operatorname{cosec} \frac{\pi}{n}$,then $m+n=$

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