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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Vedclass · Accepted Answer

$28$

Vedclass · Answer

(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 $m+n=$

Similar Questions

Let $n$ be an odd integer. If $\sin n\theta = \sum\limits_{r = 0}^n {{b_r}{{\sin }^r}\theta } $ for every value of $\theta $,then

If $\sec x = \frac{25}{24}$ and $x$ lies in the first quadrant,then $\sin \frac{x}{2} + \cos \frac{x}{2} =$

If $\text{cosec} \theta = \frac{p + q}{p - q}$,then $\cot \left( \frac{\pi}{4} + \frac{\theta}{2} \right) = $

If $\frac{1}{2}\left(\tan \left(\frac{\pi}{24}\right)+\cot \left(\frac{\pi}{24}\right)\right)=\sqrt{a^2+a}+\sqrt{a}$,then $a=$

If $\sin \alpha = \frac{336}{625}$ and $450^\circ < \alpha < 540^\circ$,then $\sin \left( \frac{\alpha}{4} \right) = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module