Question

$\tan \frac{5\pi }{12}-\tan \frac{\pi }{12}-\sqrt{3}\tan \frac{5\pi }{12}\tan \frac{\pi }{12}isequalto$

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

Answer 1

The correct option is A $\sqrt{3}$

Given,

$\tan \frac{5\pi }{12}-\tan \frac{\pi }{12}-\sqrt{3}\tan \frac{5\pi }{12}\tan \frac{\pi }{12}$

$=(2+\sqrt{3})-(2-\sqrt{3})-\sqrt{3}(2+\sqrt{3})(2-\sqrt{3})$

$=2+\sqrt{3}-2+\sqrt{3}-\sqrt{3}[2^2-(\sqrt{3}{)}^2]$

$=2\sqrt{3}-\sqrt{3}(4-3)$

$=2\sqrt{3}-\sqrt{3}$

$=\sqrt{3}$