Question

How do you find the general solutions for `tan^2x=3`?

Answer 1

`dom(tan)={x|x=pi/3+kpi,kinZZ}uu{x|x=(2pi)/3+kpi,kinZZ}`

Explanation:

`tan^2x` is equal to 3, meaning `tanx` is equal to ±`sqrt3`.

`[1]color(white)(XX)tan^2x=3`

`[2]color(white)(XX)tanx=+-sqrt3`

Now we just have to look for `x`. `+-sqrt3` is a value of tangent obtained from the special angles `pi/3`, `(2pi)/3`, `(4pi)/3`, `(5pi)/3`, and all other coterminal angles.

So we can write the solution set like this:

`dom(tan)={x|x=pi/3+kpi,kinZZ}uu{x|x=(2pi)/3+kpi,kinZZ}`