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))
