Question

Value of $\tan {15}^{\circ }$ is

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

Answer 1

Answer: (A), (B)

The correct options are
A $\frac{\sqrt{3}-1}{\sqrt{3}+1}$
B $2-\sqrt{3}$

Simplify $\tan {15}^{\circ }=\tan (45-{30}^{\circ })$

$=\frac{\tan 45-\tan {30}^{\circ }}{1+\tan 45\tan {30}^{\circ }}$

$=\frac{1-\frac{1}{\sqrt{3}}}{1+1\times \frac{1}{\sqrt{3}}}$

$=\frac{\sqrt{3}-1}{\sqrt{3}+1}$

$=2-\sqrt{3}$