Question 188358
{{{tan(3x)=1}}} Start with the given equation.



{{{3x=arctan(1)}}} Take the arctangent of both sides (to eliminate the tangent on the left side)



{{{3x=pi/4+pi*n}}} Evaluate the arctangent of 1 to get {{{pi/4}}} (use the unit circle). Remember to add {{{pi*n}}} (to account for <i>all</i> of the solutions).


Note: {{{n}}} is an integer



{{{x=(pi/4+pi*n)/3}}} Divide both sides by 3.



{{{x=pi/12+(pi*n)/3}}} Break up the fraction and simplify



So the solutions are {{{x=pi/12+(pi*n)/3}}} where "n" is an integer.