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 $\frac{(\cot A \cot B - 1)}{(\cot B + \cot A)} = x,$ then the value of $x$ is

If $5(\tan^2 x - \cos^2 x) = 2\cos 2x + 9$,then $\cos 4x$ is equal to

The value of $\cos 52^\circ + \cos 68^\circ + \cos 172^\circ$ is

$\sin (\beta + \gamma - \alpha ) + \sin (\gamma + \alpha - \beta ) + \sin (\alpha + \beta - \gamma ) - \sin (\alpha + \beta + \gamma ) = $

$\cos \frac{\pi }{7} \cos \frac{2\pi }{7} \cos \frac{4\pi }{7} = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module