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

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Answer 1 · 2015-04-22T15:38:21

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

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

$tan (\frac{x}{2})$ $color(red)( tan(x/2))$

$= \frac{\frac{5}{13}}{1 + (- \frac{12}{13})}$ $color(red)(=(5/13)/(1+(-12/13)))$

$= 5$ $color(red)(= 5)$

or

$tan (\frac{x}{2})$ $color(blue)(tan(x/2))$

$= \frac{- \frac{5}{13}}{1 + \frac{12}{13}}$ $color(blue)(=(-5/13)/(1+12/13))$

$= - \frac{1}{5}$ $color(blue)(=-1/5)$

How to solve for tan(x/2) if tanx = (-5/12)tanx=(−512)tanx = (-5/12)?