Question #e22ad

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Question #e22ad

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Answer 1 · 2017-02-13T14:32:33

$x=2npi+3pi/2$
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.

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Question #e22ad

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