Question

Which one of the following is the value of $\tan {75}^0$?

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

Answer 1

The correct option is C $\frac{\sqrt{3}+1}{\sqrt{3}-1}$

$\tan {75}^0=\tan ({45}^0+{30}^0)$
$=\frac{\tan {45}^0+\tan {30}^0}{1-\tan {45}^0\tan {30}^0}$
$=\frac{1+\tan {30}^0}{1-\tan {30}^0}$
$=\frac{1+\frac{1}{\sqrt{3}}}{1-\frac{1}{\sqrt{3}}}=\frac{\sqrt{3}+1}{\sqrt{3}-1}$