Question

How do you solve `tan(1/2x)=-1`?

Answer 1

`x=-pi/2+2kpi`

Explanation:

tan(1/2x)=-1
substitute 1/2x with `alpha`

so then you get tan( `alpha`)=-1
this is now easy to solve (because its a basic trig equality)
so `alpha`= `-pi/4` +k`pi`
if we replace `alpha` with 1/2x we get: 1/2x=`-pi/4` +k`pi`
now we have to isolate x by bringing the 2 to the other side
once we doe that, the answer is equal to `x=-pi/2+2kpi`