Question

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

Answer 1

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`:

`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)`