Question

Find all solutions of the equation. (Enter each answer in the form θ + 2πk, 0 ≤ θ < 2π. If there are any unused answer boxes, enter NONE in the last boxes.)

1-tan^2(x)=0

Answer 1

\[\tan^2(x) = 1\]

Answer 2

tan(x) = +- 1


tan(x) = 1 ->> related angle \[\pi/4\]

Answer 3

tan is postive in first and third quadrants

so \[x= \pi/4 , (\pi + \pi/4)\]

Answer 4

similarly , with the tan(x) =-1 , this gives same related angle, but we are in the other two quadrants\[x= (\pi - \pi/4 ) , (2\pi - \pi/4 )\]

Answer 5

thanks