Question

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?

Answer 1

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