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

1 Answer
Rafael
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}#

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