Find all solutions in the interval [ 0 , 2 π ) . Respond with DNE if there are none. tan 2 ( x ) − 1 = 0

Answer 1

Hard to tell if you mean tan2x -1 = 0 or tan^2(x) - 1 = 0

IF tan2x = 1 then x = pi/8 or 5pi/8

IF tan^2x = 1 then x = pi/4, 3pi/4, 5pi/4, or 7pi/4

tangent of an angle = 1 means the reference angle = 45 degrees = pi/4

that's possible in all 4 quadrants which is what you get with tan^2x = 1

but only in 2 quadrants with tan2x = 1