cos frac{pi }{7} cos frac{2pi }{7} cos frac{4 | vedclass

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

Question

(D) We use the formula $\cos 	heta \cos 2	heta \cos 4	heta \dots \cos 2^{n-1}	heta = \frac{\sin(2^n 	heta)}{2^n \sin 	heta}$.Here,$	heta = \fra

Vedclass · Accepted Answer

$-\frac{1}{8}$

Vedclass · Answer

(D) We use the formula $\cos 	heta \cos 2	heta \cos 4	heta \dots \cos 2^{n-1}	heta = \frac{\sin(2^n 	heta)}{2^n \sin 	heta}$.Here,$	heta = \frac{\pi}{7}$ and $n = 3$.Thus,$\cos \frac{\pi}{7} \cos \frac{2\pi}{7} \cos \frac{4\pi}{7} = \frac{\sin(2^3 \cdot \frac{\pi}{7})}{2^3 \sin(\frac{\pi}{7})}$.$= \frac{\sin(\frac{8\pi}{7})}{8 \sin(\frac{\pi}{7})}$.Since $\sin(\frac{8\pi}{7}) = \sin(\pi + \frac{\pi}{7}) = -\sin(\frac{\pi}{7})$.$= \frac{-\sin(\frac{\pi}{7})}{8 \sin(\frac{\pi}{7})} = -\frac{1}{8}$.

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

Similar Questions

If $x \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$,then $\log \sec x = $

If $\sin \theta = -\frac{4}{5}$ and $\theta$ lies in the third quadrant,then $\cos \frac{\theta}{2} = $

If $\cos \theta = \frac{1}{2}\left( a + \frac{1}{a} \right),$ then the value of $\cos 3\theta$ is

If $\theta$ does not lie in the second quadrant and $\tan \theta = \frac{-3}{4}$,then $\tan \frac{\theta}{2} + \sin 2 \theta =$

Find the value of $\tan \frac{\pi}{8}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module