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

1 Answer
Oct 25, 2015

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}