Question

What is the value of $\tan {75}^{\circ }$ ?

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

Answer 1

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

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