I keep trying to solve this by factring but I can't seem to get! It's so frustrating!
The problem is 1+tan2x=0
This is how I worked the problem before:
1+((2tanx)/(1-tan^2x))=0
((2tanx)/(1-tan^2x))= -1
Then I cross multiplied to get:
-1 + tan^2x = 2 tanx
Than I rearranged everything like so...
tan^2x - 2tanx -1 =0
Then I tried to factor it but it wouldn't work. Is there something wrong with my work?
Actually you don't need to simplify the tan2x. If you move 1 over to the other side to get -1 then you just need to find the tan of -1.
According to the unit circle this gives you three pi fourths + npi and 7 pi fourths + npi (remember the period of the tangent function is 2). Then just divide those two values by 2 because your equation is still equated to 2x.
Then you have your answers!
Hope this helped
It seems like you made a small mistake while rearranging the equation. The correct equation after rearranging should be:
tan^2x - 2tanx + 1 = 0
Now, let's try factoring it correctly. We have:
(tanx - 1)(tanx - 1) = 0
By factoring, we see that (tanx - 1) is a factor of 0. Therefore, we can set each factor equal to zero and solve for x:
tanx - 1 = 0 or tanx - 1 = 0
Solving each equation separately, we get:
tanx = 1 or tanx = 1
Now, to find the possible values of x, we can use the inverse tangent function (also known as arctan or tan^(-1)):
x = arctan(1) or x = arctan(1)
Using a calculator, we find that arctan(1) is π/4 radians or 45 degrees. So, the possible values of x are:
x = π/4 + πk or x = π/4 + πk (where k is an integer)
In degree mode, this becomes:
x = 45 degrees + 180k or x = 45 degrees + 180k (where k is an integer)
Therefore, the solution to the equation 1 + tan(2x) = 0 is x = 45 degrees + 180k, where k is an integer.