Question #e22ad

1 Answer
Feb 13, 2017

#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.