Question

Question #e22ad

Answer 1

`x=2npi+3pi/2`
where `n in NN`

Explanation:

Consider the given equation
`2tan(x/2)+2=0`

Let's re-arrange that equation by subtracting `2` from either side, giving us
`2tan(x/2)=-2`

Now, we see that the value `2` is multiplied on both sides, so we'll divide by `2` on both sides, giving us
`{cancel2tan(x/2)}/cancel2=-cancel2/cancel2`

We end up with `tan(x/2)=-1`

Now, the value for which the tan functions give `-1` in the range `(0,2pi)` would be either `3pi/4` or `7pi/4`

If you notice either answer, you'll see the second answer is `pi` more than the first one, that is `7pi/4=pi+3pi/4`

So, in a general case, the answers are `npi+3pi/4`

So, `x/2=npi+3pi/4`

If one were to find `x`, then by multiplying by `2`, they'll get the answer they were looking for.