Question

The value of $cos⁡(\frac{2π}{7})+cos⁡(\frac{4π}{7})+cos⁡(\frac{6π}{7})$ is equal to:

• A. $-1$
• B. $-\frac{1}{2}$
• C. $-\frac{1}{3}$
• D. $-\frac{1}{4}$

Answer 1

Answer: (B)

$-\frac{1}{2}$

Answer 2

$cos⁡(\frac{2π}{7})+cos⁡(\frac{4π}{7})+cos⁡(\frac{6π}{7})$

$= \frac{sin3(\frac{π}{7})}{sin\frac{π}{7}} cos \frac{(\frac{2π}{7}+\frac{6π}{7})}{2}$

$= \frac{sin(\frac{3π}{7}).cos(\frac{4π}{7})}{sin(\frac{π}{7})}$

= $\frac{2sin\frac{4π}{7}.cos\frac{4π}{7}}{2sin \frac{π}{7}}$

= $\frac{sin(\frac{8π}{7})}{2sin\frac{π}{7}}$

= $\frac{-sin\frac{π}{7}}{2sin\frac{π}{7}}$

=$\frac{-1}{2}$

Hence, the correct option is (B): $-\frac{1}{2}$