What is the general solution for (2tan(x))/(1-tan^2(x))=sqrt(3) ?

The general solution for (2tan(x))/(1-tan^2(x))=sqrt(3) is x=(2pi)/3+pin,x= pi/6+pin

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(2tan(x))/(1-tan^2(x))=sqrt(3)

\frac{2 tan ( x )}{1 - tan ^{2} ( x )} = 3

x = \frac{2 π}{3} + πn, x = \frac{π}{6} + πn

Solution steps

\frac{2 tan ( x )}{1 - tan ^{2} ( x )} = 3

Solve by substitution

tan (x) = - 3, tan (x) = \frac{3}{3}

tan (x) = - 3 : x = \frac{2 π}{3} + πn

tan (x) = \frac{3}{3} : x = \frac{π}{6} + πn

Combine all the solutions

x = \frac{2 π}{3} + πn, x = \frac{π}{6} + πn

tan (x) = \frac{59}{56}

cos (θ) = \frac{5}{5 2}

arccos (x) = arcsin (\frac{9}{41})

x, - y sin (x) = 0

2 sin (\frac{x}{2} + \frac{π}{3}) = 3

What is the general solution for (2tan(x))/(1-tan^2(x))=sqrt(3) ?
The general solution for (2tan(x))/(1-tan^2(x))=sqrt(3) is x=(2pi)/3+pin,x= pi/6+pin