What is the general solution for tan^2(6x)=3 ?

The general solution for tan^2(6x)=3 is x= pi/(18)+(pin)/6 ,x= pi/9+(pin)/6

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tan^2(6x)=3

tan^{2} (6 x) = 3

x = \frac{π}{18} + \frac{πn}{6}, x = \frac{π}{9} + \frac{πn}{6}

Solution steps

tan^{2} (6 x) = 3

Solve by substitution

tan (6 x) = 3, tan (6 x) = - 3

tan (6 x) = 3 : x = \frac{π}{18} + \frac{πn}{6}

tan (6 x) = - 3 : x = \frac{π}{9} + \frac{πn}{6}

Combine all the solutions

x = \frac{π}{18} + \frac{πn}{6}, x = \frac{π}{9} + \frac{πn}{6}

tan (2 x) = 3 sin (2 x)

sin (x) tan (x) = \frac{3}{2}

sec^{2} (x) + 2 = 6

4 sin (x) + 1 = 2 sin (x)

\frac{sin ( 2 x )}{cos ( x )} = 1

What is the general solution for tan^2(6x)=3 ?
The general solution for tan^2(6x)=3 is x= pi/(18)+(pin)/6 ,x= pi/9+(pin)/6