Question

$\tan \frac{2\pi }{5}-\tan \frac{\pi }{15}-\sqrt{3}\tan \frac{2\pi }{5}\tan \frac{\pi }{15}$ is equal to

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

Answer 1

Answer: (A)

Now $\frac{2\pi }{5}-\frac{\pi }{15}=\frac{\pi }{3}$
$\Rightarrow \tan \frac{2\pi }{5}-\frac{\pi }{15}=\tan \frac{\pi }{3}$
$\Rightarrow \frac{\tan \frac{2\pi }{5}-\tan \frac{\pi }{15}}{1+\tan \frac{2\pi }{5}\tan \frac{\pi }{15}}=\sqrt{3}$