Acute angle between the lines whose slopes are ${\mathrm{m}}_1=2,{\mathrm{m}}_2=\frac{1}{2}$  is  $\theta$ then the value of $\mathrm{tan\theta }$ is

If  be the acute angle between two lines having slopes ${\mathrm{m}}_1$  and ${\mathrm{m}}_2$ then  $\mathrm{tan\theta }=\left|\frac{{\mathrm{m}}_1-{\mathrm{m}}_2}{1+{\mathrm{m}}_1{\mathrm{m}}_2}\right|$
Hence,

$\begin{array}{c}\tan \theta =\left|\frac{2-\frac{1}{2}}{1+1}\right|\\ =\frac{3}{4}\end{array}$

Therefore,$\tan \theta =\boxed{0.75}$