Question

What is $\tan {15}^o$ equal to?

• A. $2-\sqrt{3}$
• B. $2+\sqrt{3}$
• C. $1-\sqrt{3}$
• D. $1+\sqrt{3}$

Answer 1

The correct option is A $2-\sqrt{3}$

We know that $\tan 2x=\frac{2\tan x}{1-{\tan }^{2}x}$

When $x={15}^o$, we have

$\tan \left({30}^o\right)=\frac{2\tan {15}^o}{1-{\tan }^2{15}^o}$

$\Rightarrow \frac{1}{\sqrt{3}}=\frac{2\tan {15}^o}{1-{\tan }^2{15}^o}$

$\Rightarrow {\tan }^2{15}^o+2\sqrt{3}\tan {15}^o-1=0$

$\therefore \tan {15}^o=\frac{-2\sqrt{3}\pm \sqrt{{(-2\sqrt{3})}^2-(4\times 1(-1\left)\right)}}{2}$

$\Rightarrow \tan {15}^o=\frac{-2\sqrt{3}\pm 4}{2}=2-\sqrt{3},-2-\sqrt{3}$