SOLUTION: Solve [0<=x<=2pi] (tanx+tan(pi/3))/(1-tanxtan(pi/3))={{{sqrt(3)}}}

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Question 888406: Solve [0<=x<=2pi]
(tanx+tan(pi/3))/(1-tanxtan(pi/3))=sqrt%283%29
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
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))

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