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

The maximum value of the function $f(x) = 3\sin x + 4\cos x$ is

The minimum value of $3\sin \theta + 4\cos \theta$ is

$\log _{\frac{1}{8}\csc^2 \frac{\pi}{8}} \sin^2 \frac{3\pi}{8}$ equals to

The value of $\cos^2 \frac{\pi}{12} + \cos^2 \frac{\pi}{4} + \cos^2 \frac{5\pi}{12}$ is

The value of $x$ for the maximum value of $(\sqrt{3} \sin x + \cos x)$ is .....$^o$

Vedclass Test Series

Exam Paper Generator

Online Exam Module