Answer
False
Work Step by Step
Testing the equation: $\tan{\dfrac{A}{2}} = \dfrac{\tan{A}}{2}$ for $A=60^\circ$
$LHS = \tan{30} =\dfrac{\sqrt{3}}{3}$
$RHS = \dfrac{\tan{60}}{2}= \dfrac{\sqrt{3}}{2}$
$LHS \neq RHS$
$\tan{\dfrac{A}{2}} \neq \dfrac{\tan{A}}{2}$