Question

show that cos 2 pie by 7 cos 4 pie by 7 cos 8 pie by 7 is equal to 1 by 8​

Answer 1

Step-by-step explanation:

$= cos \frac{2\pi}{7} cos \frac{4\pi}{7} cos \frac{8\pi}{7} \\ As \: we \: know \: that \: \\ cos \alpha \: cos2 \alpha cos {2}^{2} \alpha .........cos {2}^{n - 1} \alpha = \frac{sin {2}^{n} \alpha }{ {2}^{n} sin \alpha } \\ \alpha = \frac{2\pi}{7} \: \: \: n = 3 \\ = \frac{sin \frac{16\pi}{7} }{8sin \frac{2\pi}{7} } \\ = \frac{sin(2\pi + \frac{2\pi}{7}) }{8sin \frac{2\pi}{7} } \\ = \frac{sin \frac{2\pi}{7} }{8sin \frac{2\pi}{7} } \\ = \frac{1}{8} \\ Hence \: proved... \\ hope \: it \: will \: help \: you...... \:$