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

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

Question

(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

Vedclass · Accepted Answer

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

Vedclass · Answer

(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:

Similar Questions

If $\frac{1+\cos A}{1-\cos A}=\frac{m^{2}}{n^{2}}$,then $\tan A=$

If $\sin x + \cos x = \frac{1}{5},$ then $\tan 2x$ is

$\tan 5^{\circ} \tan 25^{\circ} \tan 45^{\circ} \tan 65^{\circ} \tan 85^{\circ} = $

$2\sin^2 \beta + 4\cos(\alpha + \beta)\sin \alpha \sin \beta + \cos 2(\alpha + \beta) = $

If $0 < \theta < \pi$,then the minimum value of $3\sin \theta + \csc^3 \theta$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module