Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

$\cos \frac{2\pi }{7}+\cos \frac{4\pi }{7}+\cos \frac{6\pi }{7}=\frac{2\sin \frac{\pi }{7}\cos \frac{2\pi }{7}+2\sin \frac{\pi }{7}\cos \frac{4\pi }{7}+2\sin \frac{\pi }{7}\cos \frac{6\pi }{7}}{2\sin \frac{\pi }{7}}$ $=\frac{\left(\sin \frac{3\pi }{7}-\sin \frac{\pi }{7}\right)+\left(\sin \frac{5\pi }{7}-\sin \frac{3\pi }{7}\right)+\left(\sin \pi -\sin \frac{5\pi }{7}\right)}{2\sin \frac{\pi }{7}}=\frac{-\sin \frac{\pi }{7}}{2\sin \frac{\pi }{7}}=-\frac{1}{2}$. Hence the required value $=-2\times \left(-\frac{1}{2}\right)=1$.