Question

The value of tan ${75}^0$ is

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

Answer 1

Answer: (C)

$2+\sqrt{3}$

$\tan {75}^{\circ }=\tan ({45}^{\circ }+{30}^{\circ })=\frac{\tan {45}^{\circ }+\tan {30}^{\circ }}{1-\tan {45}^{\circ }.\tan {30}^{\circ }}=\frac{1+\frac{1}{\sqrt{3}}}{1-\frac{1}{\sqrt{3}}}=\frac{\sqrt{3}+1}{\sqrt{3}-1}\times \frac{\sqrt{3}+1}{\sqrt{3}+1}=\frac{{(\sqrt{3}+1)}^2}{3-1}=2+\sqrt{3}$