Question

The slope of the line which is inclined at an angle of ${75}^{\circ }$ with the $x-$axis in anticlockwise direction is

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

Answer 1

The correct option is B $2+\sqrt{3}$

Slope of a line $m=\tan \theta$
Where $\theta$ is the inclination with $x-$axis in anticlockwise direction
$\Rightarrow m=\tan {75}^{\circ }=\tan ({45}^{\circ }+{30}^{\circ })=\frac{\tan {45}^{\circ }+\tan {30}^{\circ }}{1-\tan {45}^{\circ }\tan {30}^{\circ }}$
$=\frac{1+\frac{1}{\sqrt{3}}}{1-\frac{1}{\sqrt{3}}}$
$=\frac{\sqrt{3}+1}{\sqrt{3}-1}$
$=2+\sqrt{3}$