Question

$\cos \frac{\pi }{7}+\cos \frac{2\pi }{7}+\cos \frac{3\pi }{7}+\cos \frac{4\pi }{7}+\cos \frac{5\pi }{7}+\cos \frac{6\pi }{7}=$

• A. 0
• B. 1
• C. -1
• D. 2

Answer 1

The correct option is A 0

Given,

$\cos \frac{\pi }{7}+\cos \frac{2\pi }{7}+\cos \frac{3\pi }{7}+\cos \frac{4\pi }{7}+\cos \frac{5\pi }{7}+\cos \frac{6\pi }{7}$

$=(\cos \frac{\pi }{7}+\cos \frac{6\pi }{7})+(\cos \frac{2\pi }{7}+\cos \frac{5\pi }{7})+(\cos \frac{3\pi }{7}+\cos \frac{4\pi }{7}+)$

$=2\cos \frac{\pi }{2}\cos (-\frac{5\pi }{14})+2\cos \frac{\pi }{2}\cos (-\frac{3\pi }{14})+2\cos \frac{\pi }{2}\cos (-\frac{\pi }{14})$

But, $\cos \frac{\pi }{2}=0$

$=2\left(0\right)+2\left(0\right)+2\left(0\right)=0$