Question

$\tan \frac{\pi }{11}+\tan \frac{2\pi }{11}+\tan \frac{4\pi }{11}+\tan \frac{7\pi }{11}+\tan \frac{9\pi }{11}+\tan \frac{10\pi }{11}$.

Answer 1

$=\tan \frac{\pi }{11}+\tan \frac{2\pi }{11}+......+\tan \frac{10\pi }{11}$

$=\tan \frac{\pi }{11}+\tan \frac{2\pi }{11}+......+\tan (\pi -\frac{\pi }{11})$

$=\tan \frac{\pi }{11}+\tan \frac{2\pi }{11}+......\tan \frac{\pi }{11}$

$=0$