Question 888406
it appears the solution to this is x = 0 +/- pi.


tan(pi/3) is equal to sqrt(3).


you can confirm this using your calculator.


calculate tan(pi/3) and then square the answer.   you should get 3.


make sure your calculator is in radian mode.


your equation of:


(tan(x) + tan(pi/3))/(1 - tan(x) * tan(pi/3))= sqrt(3) becomes:


(tan(x) + sqrt(3)) / (1 - tan(x) * sqrt(3)) = sqrt(3)


multiply both sides of this equation by (1 - tan(x) * sqrt(3)) to get:


tan(x) + sqrt(3) = sqrt(3) * (1 - tan(x) * sqrt(3))


simplify to get:


tan(x) + sqrt(3) = sqrt(3) - 3 * tan(x)


add 3 * tan(x) to both sides of the equation and subtract sqrt(3) from both sides of the equation to get:


4 * tan(x) = 0


divide both sides of the equation by 4 to get:


tan(x) = 0


tan(x) is equal to 0 when x = 0  +/- pi * k where k is equal to any non-negative integer.


the following graph shows you a picture of the 2 equations and the points where they intersect.


their intersections is the solution.


one of the equations is y = sqrt(3).


the other of the equations is y = (tan(x) + tan(pi/3))/(1 - tan(x) * tan(pi/3))


<img src = "http://theo.x10hosting.com/2014/072901.jpg" alt="$$$" </>