How to solve for tan(x/2) if $tanx = (-5/12)$ ?

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Answer 1 · 2015-04-22T15:38:21

The Half-angle formula for $tan$ is
$tan(x/2) = (sin(x))/(1+cos(x))$

From the diagram for the possibilities for $tan(x) = -5/12$ :
enter image source here

$color(red)( tan(x/2))$

$color(red)(=(5/13)/(1+(-12/13)))$

$color(red)(= 5)$

or

$color(blue)(tan(x/2))$

$color(blue)(=(-5/13)/(1+12/13))$

$color(blue)(=-1/5)$

How to solve for tan(x/2) if tanx = (-5/12)tanx = (-5/12)?